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1
Cutsets and anti-chains in linear lattices
Dergi Makalesi

Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Journal of Combinatorial Theory, Series A
Yayıncı:
Elsevier
Yazar(lar) :
Bruce Rothschild , Shahriar Shahriari
Yıl :
2006
Journal of Combinatorial Theory, Series A
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Consider the poset, ordered by inclusion, of subspaces of a four-dimensional vector space over a field with 2 elements. We prove that, for this poset, any cutset (i.e., a collection of elements that intersects every maximal chain) contains a maximal anti-chain of the poset. In analogy with the same result by Duffus, Sands, and Winkler [D. Duffus, B. Sands, P. Winkler, Maximal chains and anti-chains in Boolean lattices, SIAM J. Discrete Math. 3 (2) (1990) 197–205] for the subset lattice, we conjecture that the above statement holds in any dimension and for any finite base field, and we prove some special cases to support the conjecture.
DOI : 10.1016/j.jcta.2006.03.022
Anahtar Kelimeler : Cutset, Anti-chain, Fibre, Maximal chain, Linear lattice, Projective geometry, PG(n, q)
ISSN: 0097-3165
Sayı: 8
Cilt: 113
Sayfa: 1783-1790
Sınıflandırma :
2
Editorial Board
Dergi Makalesi

Dergi Makalesi
Kaynak 1:
Science Direct
Kaynak 2:
Science Direct
Dergi:
Journal of Combinatorial Theory, Series A
Yayıncı:
Elsevier
Yıl :
2007
Journal of Combinatorial Theory, Series A
Tam Metin
Kaydet Alıntıla
DOI : 10.1016/s0097-3165(07)00065-9
ISSN: 0097-3165
Sayı: 6
Cilt: 114
Sayfa: i
3
Independence polynomials and Alexander-Conway polynomials of plumbing links
Dergi Makalesi

Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Journal of Combinatorial Theory, Series A
Yayıncı:
Elsevier BV
Yazar(lar) :
A. Stoimenow
Yıl :
2021
Journal of Combinatorial Theory, Series A
Yayıncı Web Sitesi
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Kaydet Alıntıla
We use the Chudnovsky-Seymour Real Root Theorem for independence polynomials to obtain some statements about the coefficients and roots of the Alexander and Conway polynomial of some types of plumbing links, addressing conjectures of Fox, Hoste and Liechti.
DOI : 10.1016/j.jcta.2021.105487
Anahtar Kelimeler : Independence polynomial, Line graph, Polynomial root, Alternating knot, Alexander polynomial, Arborescent link, 2-bridge link
ISSN: 0097-3165
Cilt: 183
Sayfa: 105487
4
Strongly regular Cayley graphs with λ − μ = −1
Dergi Makalesi

Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Journal of Combinatorial Theory, Series A
Yayıncı:
Elsevier
Yazar(lar) :
K.T Arasu , D Jungnickel , S.L Ma , A Pott
Yıl :
1994
Journal of Combinatorial Theory, Series A
Yayıncı Web Sitesi
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Kaydet Alıntıla
The classification problem for strongly regular graphs for which the parameters are related by the equation λ − μ = −1 is still completely open. Restricting attention to those examples which are simultaneously Cayley graphs based on an abelian group (which are equivalent to abelian partial difference sets with λ − μ = −1), we obtain the following classification result: any such graph is—up to complementation—either of Paley type (i.e., it has parameters (ν, (ν − 1)/2, (ν − 5)/4, (ν − 1)/4)) or it has parameters (243, 22, 1, 2). The proof of this theorem combines recent results on the structure of partial difference sets with some results concerning diophantine equations. Our theorem has interesting applications to the theory of divisible difference sets, since it allows us to improve previous classification results concerning abalian DDS's satisfying k − λ1 = 1 and reversible abelian DDS's.
DOI : 10.1016/0097-3165(94)90007-8
ISSN: 0097-3165
Sayı: 1
Cilt: 67
Sayfa: 116-125
Sınıflandırma :
5
An extremal problem for finite topologies and distributive lattices
Dergi Makalesi

Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Journal of Combinatorial Theory, Series A
Yayıncı:
Elsevier
Yazar(lar) :
Richard P Stanley
Yıl :
1973
Journal of Combinatorial Theory, Series A
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Let (r1, r2, …) be a sequence of non-negative integers summing to n. We determine under what conditions there exists a finite distributive lattice L of rank n with ri join-irreducibles of rank i, for all i = 1, 2, …. When L exists, we give explicit expressions for the greatest number of elements L can have of any given rank, and for the greatest total number of elements L can have. The problem is also formulated in terms of finite topological spaces.
DOI : 10.1016/0097-3165(73)90022-8
ISSN: 0097-3165
Sayı: 2
Cilt: 14
Sayfa: 209-214
Sınıflandırma :
6
Strictness of the log-concavity of generating polynomials of matroids
Dergi Makalesi

Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Journal of Combinatorial Theory, Series A
Yayıncı:
Elsevier BV
Yazar(lar) :
Satoshi Murai , Takahiro Nagaoka , Akiko Yazawa
Yıl :
2021
Journal of Combinatorial Theory, Series A
Yayıncı Web Sitesi
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Kaydet Alıntıla
Recently, it was proved by Anari–Oveis Gharan–Vinzant, Anari–Liu–Oveis Gharan–Vinzant and Brändén–Huh that, for any matroid M, its basis generating polynomial and its independent set generating polynomial are log-concave on the positive orthant. Using these, they obtain some combinatorial inequalities on matroids including a solution of strong Mason's conjecture. In this paper, we study the strictness of the log-concavity of these polynomials and determine when equality holds in these combinatorial inequalities. We also consider a generalization of our result to morphisms of matroids.
DOI : 10.1016/j.jcta.2020.105351
Anahtar Kelimeler : Matroid, Independent set, Mason's conjecture, Lorentzian polynomial, Hodgeu2013Riemann relation, Morphism of matroids
ISSN: 0097-3165
Cilt: 181
Sayfa: 105351
7
Intervals in Catalan lattices and realizers of triangulations
Dergi Makalesi

Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Journal of Combinatorial Theory, Series A
Yayıncı:
Elsevier
Yazar(lar) :
Olivier Bernardi , Nicolas Bonichon
Yıl :
2009
Journal of Combinatorial Theory, Series A
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Kaydet Alıntıla
The Stanley lattice, Tamari lattice and Kreweras lattice are three remarkable orders defined on the set of Catalan objects of a given size. These lattices are ordered by inclusion: the Stanley lattice is an extension of the Tamari lattice which is an extension of the Kreweras lattice. The Stanley order can be defined on the set of Dyck paths of size n as the relation of being above. Hence, intervals in the Stanley lattice are pairs of non-crossing Dyck paths. In a previous article, the second author defined a bijection Φ between pairs of non-crossing Dyck paths and the realizers of triangulations (or Schnyder woods). We give a simpler description of the bijection Φ. Then, we study the restriction of Φ to Tamari and Kreweras intervals. We prove that Φ induces a bijection between Tamari intervals and minimal realizers. This gives a bijection between Tamari intervals and triangulations. We also prove that Φ induces a bijection between Kreweras intervals and the (unique) realizers of stack triangulations. Thus, Φ induces a bijection between Kreweras intervals and stack triangulations which are known to be in bijection with ternary trees.
DOI : 10.1016/j.jcta.2008.05.005
Anahtar Kelimeler : Tamari lattice, Kreweras lattice, Stanley lattice, Schnyder woods, Triangulations, Bijection
ISSN: 0097-3165
Sayı: 1
Cilt: 116
Sayfa: 55-75
Sınıflandırma :
8
Some hidden relations involving the ten symmetry classes of plane partitions
Dergi Makalesi

Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Journal of Combinatorial Theory, Series A
Yayıncı:
Elsevier
Yazar(lar) :
John R Stembridge
Yıl :
1994
Journal of Combinatorial Theory, Series A
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Kaydet Alıntıla
Let B be a partially ordered product of three finite chains. For any group G of automorphisms of B, let NG(B, q) denote the rank generating function for G-invariant order ideals of B. If we regard B as a rectangular prism, NG(B, q) can be viewed as a generating function for plane partitions that fit inside B. Similarly, define NG′(B, q) to be the rank generating function for order ideals of the quotient poset BG. We prove that NG(B, − 1) and NG′(B, − 1) count the number of plane partitions (i.e., order ideals of B) that are invariant under certain automorphisms and complementation operations on B. Consequently, one discovers that the number of plane partitions belonging to each of the ten symmetry classes identified by Stanley is of the form NG(B, ± 1) or NG′(B, ± 1) for some subgroup G of S3, and conversely. We also discuss the occurrence of this phenomenon in general partially ordered sets, and use the theory of P-partitions to derive a criterion for one aspect of it.
DOI : 10.1016/0097-3165(94)90112-0
ISSN: 0097-3165
Sayı: 2
Cilt: 68
Sayfa: 372-409
Sınıflandırma :
9
On an inequality of A. Khintchine for zero-one matrices
Dergi Makalesi

Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Journal of Combinatorial Theory, Series A
Yayıncı:
Elsevier
Yazar(lar) :
W.A.J Luxemburg
Yıl :
1972
Journal of Combinatorial Theory, Series A
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Kaydet Alıntıla
Let A be a matrix of m rows and n columns whose entries are either zero or one with row i of sum ri (i = 1, 2,…, m) and column j of sum sj (j = 1, 2,…, n). Then a result of Khintchine states that Σi = 1m ri2 + Σj = 1n sj2 ⩽ σ(l + σl), where l = max(m, n) and σ is the total number of ones in A. In the present paper a new proof of Khintchine's inequality is presented and a number of extensions to bounded plane measurable sets are discussed.
DOI : 10.1016/0097-3165(72)90043-x
ISSN: 0097-3165
Sayı: 2
Cilt: 12
Sayfa: 289-296
Sınıflandırma :
Matematik %100
10
Structural submodularity and tangles in abstract separation systems
Dergi Makalesi

Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Journal of Combinatorial Theory, Series A
Yayıncı:
Elsevier
Yazar(lar) :
Reinhard Diestel , Joshua Erde , Daniel Weißauer
Yıl :
2019
Journal of Combinatorial Theory, Series A
Yayıncı Web Sitesi
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Kaydet Alıntıla
We prove a tree-of-tangles theorem and a tangle-tree duality theorem for abstract separation systems S→ that are submodular in the structural sense that, for every pair of oriented separations, S→ contains either their meet or their join defined in some universe U→ of separations containing S→. This holds, and is widely used, if U→ comes with a submodular order function and S→ consists of all its separations up to some fixed order. Our result is that for the proofs of these two theorems, which are central to abstract tangle theory, it suffices to assume the above structural consequence for S→, and no order function is needed.
DOI : 10.1016/j.jcta.2019.05.001
Anahtar Kelimeler : separation systems, Tree-decompositions, Graph minors, Tangles, Cluster analysis, Phylogenetic trees
ISSN: 0097-3165
Cilt: 167
Sayfa: 155-180
Sınıflandırma :
11
Ternary and binary codes for a plane of order 12
Dergi Makalesi

Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Journal of Combinatorial Theory, Series A
Yayıncı:
Elsevier
Yazar(lar) :
Marshall Hall , John Wilkinson
Yıl :
1984
Journal of Combinatorial Theory, Series A
Yayıncı Web Sitesi
Tam Metin
Kaydet Alıntıla
DOI : 10.1016/0097-3165(84)90004-9
ISSN: 0097-3165
Sayı: 2
Cilt: 36
Sayfa: 183-203
Sınıflandırma :
12
Almost-Fisher families
Dergi Makalesi

Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Journal of Combinatorial Theory, Series A
Yayıncı:
Elsevier
Yazar(lar) :
Shagnik Das , Benny Sudakov , Pedro Vieira
Yıl :
2016
Journal of Combinatorial Theory, Series A
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Kaydet Alıntıla
A classic theorem in combinatorial design theory is Fisher's inequality, which states that a family F of subsets of [n] with all pairwise intersections of size λ can have at most n non-empty sets. One may weaken the condition by requiring that for every set in F, all but at most k of its pairwise intersections have size λ. We call such families k-almost λ-Fisher. Vu was the first to study the maximum size of such families, proving that for k=1 the largest family has 2n−2 sets, and characterising when equality is attained. We substantially refine his result, showing how the size of the maximum family depends on λ. In particular we prove that for small λ one essentially recovers Fisher's bound. We also solve the next open case of k=2 and obtain the first non-trivial upper bound for general k.
DOI : 10.1016/j.jcta.2015.10.003
Anahtar Kelimeler : Design theory, Fisher's inequality, Extremal set theory, Extremal combinatorics, Hadamard matrices
ISSN: 0097-3165
Cilt: 138
Sayfa: 175-207
Sınıflandırma :
13
Constructing permutations of finite fields via linear translators
Dergi Makalesi

Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Journal of Combinatorial Theory, Series A
Yayıncı:
Elsevier
Yazar(lar) :
Gohar M. Kyureghyan
Yıl :
2011
Journal of Combinatorial Theory, Series A
Yayıncı Web Sitesi
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Kaydet Alıntıla
Methods for constructing large families of permutation polynomials of finite fields are introduced. For some of these permutations the cycle structure and the inverse mapping are determined. The results are applied to lift minimal blocking sets of PG(2,q) to those of PG(2,qn).
DOI : 10.1016/j.jcta.2010.08.005
Anahtar Kelimeler : Finite field, Permutation polynomial, Cycle structure, Complete mapping, Linear translator, Linear structure, Blocking set of Rédei type
ISSN: 0097-3165
Sayı: 3
Cilt: 118
Sayfa: 1052-1061
Sınıflandırma :
14
Orthogonal quadruple systems and 3-frames
Dergi Makalesi

Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Journal of Combinatorial Theory, Series A
Yayıncı:
Elsevier
Yazar(lar) :
William B. Muse , K.T. Phelps
Yıl :
2003
Journal of Combinatorial Theory, Series A
Yayıncı Web Sitesi
Tam Metin
Kaydet Alıntıla
Orthogonal quadruple systems are defined and investigated. Orthogonal quadruple systems with an additional nesting property are shown to provide a new construction of 3-frames F(3,4,n{2}) (Design Codes Cryptogr. 4 (1994) 5). Constructions for pairs of nested orthogonal quadruple systems are provided. Applications to 2-resolvable Steiner quadruple systems and highly nonlinear functions are discussed.
DOI : 10.1016/s0097-3165(03)00135-3
Anahtar Kelimeler : Steiner quadruple systems, Frames, Hamming code
ISSN: 0097-3165
Sayı: 1
Cilt: 104
Sayfa: 115-124
Sınıflandırma :
15
A generalization of an inequality of Brouwer–Wilbrink
Dergi Makalesi

Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Journal of Combinatorial Theory, Series A
Yayıncı:
Elsevier
Yazar(lar) :
Akira Hiraki , Jack Koolen
Yıl :
2005
Journal of Combinatorial Theory, Series A
Yayıncı Web Sitesi
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Kaydet Alıntıla
Brouwer and Wilbrink showed that t+1⩽(s2+1)cd-1 holds for a regular near 2d-gon of order (s,t) with s⩾2 and where the diameter d is even. In this note we generalize their inequality to all diameter.
DOI : 10.1016/j.jcta.2004.07.011
Anahtar Kelimeler : Distance-regular graphs, Regular near polygons, Absolute bound, Krein parameters
ISSN: 0097-3165
Sayı: 1
Cilt: 109
Sayfa: 181-188
Sınıflandırma :
Felsefe %49
Mantık %100
16
On the theorem of Feit-Higman
Dergi Makalesi

Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Journal of Combinatorial Theory, Series A
Yayıncı:
Elsevier
Yazar(lar) :
Robert Kilmoyer , Louis Solomon
Yıl :
1973
Journal of Combinatorial Theory, Series A
Yayıncı Web Sitesi
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Kaydet Alıntıla
We let correspond to any finite incidence structure S a certain semisimple algebra of endomorphisms of the vector space spanned by the flags of S. In case the structure is a generalized polygon we compute the irreducible representations of the algebra and deduce the theorem of Feit-Higman.
DOI : 10.1016/0097-3165(73)90076-9
ISSN: 0097-3165
Sayı: 3
Cilt: 15
Sayfa: 310-322
Sınıflandırma :
17
Representation of the positive real numbers as sums of colored rational numbers
Dergi Makalesi

Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Journal of Combinatorial Theory, Series A
Yayıncı:
Elsevier
Yazar(lar) :
J.-M Brochet
Yıl :
1992
Journal of Combinatorial Theory, Series A
Yayıncı Web Sitesi
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Kaydet Alıntıla
Let an arbitrary coloring of the positive rational numbers be given. We show that every positive real number is an infinite sum of distinct rational numbers which either all have the same color, or all have different colors. This answers a question of Erdős and Lefmann.
DOI : 10.1016/0097-3165(92)90044-u
ISSN: 0097-3165
Sayı: 1
Cilt: 60
Sayfa: 140-142
Sınıflandırma :
18
Toeplitz minors and specializations of skew Schur polynomials
Dergi Makalesi

Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Journal of Combinatorial Theory, Series A
Yayıncı:
Elsevier
Yazar(lar) :
David García-García , Miguel Tierz
Yıl :
2020
Journal of Combinatorial Theory, Series A
Yayıncı Web Sitesi
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Kaydet Alıntıla
We express minors of Toeplitz matrices of finite and large dimension in terms of symmetric functions. Comparing the resulting expressions with the inverses of some Toeplitz matrices, we obtain explicit formulas for a Selberg-Morris integral and for specializations of certain skew Schur polynomials.
DOI : 10.1016/j.jcta.2019.105201
Anahtar Kelimeler : Toeplitz minor, Skew Schur polynomial, Fisher-Hartwig singularity, Toeplitz inverse
ISSN: 0097-3165
Cilt: 172
Sayfa: 105201
Sınıflandırma :
19
Combinatorial characterizations of the Cohen–Macaulayness of the second power of edge ideals
Dergi Makalesi

Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Journal of Combinatorial Theory, Series A
Yayıncı:
Elsevier
Yazar(lar) :
Dô Trong Hoang , Nguyên Công Minh , Trân Nam Trung
Yıl :
2013
Journal of Combinatorial Theory, Series A
Yayıncı Web Sitesi
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Kaydet Alıntıla
Let I(G) be the edge ideal of a simple graph G. In this paper, we will give sufficient and necessary combinatorial conditions of G in which the second symbolic and ordinary power of its edge ideal are Cohen–Macaulay (resp. Buchsbaum, generalized Cohen–Macaulay). As an application of our results, we will classify all bipartite graphs in which the second (symbolic) powers are Cohen–Macaulay (resp. Buchsbaum, generalized Cohen–Macaulay).
DOI : 10.1016/j.jcta.2013.02.008
Anahtar Kelimeler : Symbolic powers, Edge ideal, Cohenu2013Macaulay, Buchsbaum, Generalized Cohenu2013Macaulay, Bipartite graphs
ISSN: 0097-3165
Sayı: 5
Cilt: 120
Sayfa: 1073-1086
Sınıflandırma :
20
From Bruhat intervals to intersection lattices and a conjecture of Postnikov
Dergi Makalesi

Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Journal of Combinatorial Theory, Series A
Yayıncı:
Elsevier
Yazar(lar) :
Axel Hultman , Svante Linusson , John Shareshian , Jonas Sjöstrand
Yıl :
2009
Journal of Combinatorial Theory, Series A
Yayıncı Web Sitesi
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Kaydet Alıntıla
We prove the conjecture of A. Postnikov that (A) the number of regions in the inversion hyperplane arrangement associated with a permutation w∈Sn is at most the number of elements below w in the Bruhat order, and (B) that equality holds if and only if w avoids the patterns 4231, 35142, 42513 and 351624. Furthermore, assertion (A) is extended to all finite reflection groups. A byproduct of this result and its proof is a set of inequalities relating Betti numbers of complexified inversion arrangements to Betti numbers of closed Schubert cells. Another consequence is a simple combinatorial interpretation of the chromatic polynomial of the inversion graph of a permutation which avoids the above patterns.
DOI : 10.1016/j.jcta.2008.09.001
Anahtar Kelimeler : Bruhat order, Inversion arrangements, Pattern avoidance
ISSN: 0097-3165
Sayı: 3
Cilt: 116
Sayfa: 564-580
Sınıflandırma :
21
All hyperbolic Coxeter n-cubes
Dergi Makalesi

Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Journal of Combinatorial Theory, Series A
Yayıncı:
Elsevier
Yazar(lar) :
Matthieu Jacquemet , Steven T. Tschantz
Yıl :
2018
Journal of Combinatorial Theory, Series A
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Kaydet Alıntıla
Beside simplices, n-cubes form an important class of simple polyhedra. Unlike hyperbolic Coxeter simplices, hyperbolic Coxeter n-cubes are not classified. We show that there is no hyperbolic Coxeter n-cube for n≥6, and provide a full classification for n≤5. Our methods, which are essentially of combinatorial and algebraic nature, can be (and have been successfully) implemented in a symbolic computation software such as Mathematica®.
DOI : 10.1016/j.jcta.2018.04.001
Anahtar Kelimeler : Hyperbolic Coxeter n-cubes, Classification of hyperbolic Coxeter polyhedra, Combinatorial enumerations, Gröbner bases
ISSN: 0097-3165
Cilt: 158
Sayfa: 387-406
Sınıflandırma :
22
Co-degree density of hypergraphs
Dergi Makalesi

Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Journal of Combinatorial Theory, Series A
Yayıncı:
Elsevier
Yazar(lar) :
Dhruv Mubayi , Yi Zhao
Yıl :
2007
Journal of Combinatorial Theory, Series A
Yayıncı Web Sitesi
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Kaydet Alıntıla
For an r-graph H, let C(H)=minSd(S), where the minimum is taken over all (r−1)-sets of vertices of H, and d(S) is the number of vertices v such that S∪{v} is an edge of H. Given a family F of r-graphs, the co-degree Turán number co-ex(n,F) is the maximum of C(H) among all r-graphs H which contain no member of F as a subhypergraph. Define the co-degree density of a family F to be γ(F)=lim supn→∞co-ex(n,F)n. When r⩾3, non-zero values of γ(F) are known for very few finite r-graphs families F. Nevertheless, our main result implies that the possible values of γ(F) form a dense set in [0,1). The corresponding problem in terms of the classical Turán density is an old question of Erdős (the jump constant conjecture), which was partially answered by Frankl and Rödl [P. Frankl, V. Rödl, Hypergraphs do not jump, Combinatorica 4 (2–3) (1984) 149–159]. We also prove the existence, by explicit construction, of finite F satisfying 0<γ(F)
DOI : 10.1016/j.jcta.2006.11.006
Anahtar Kelimeler : Codegree, Jump constant, Hypergraph, Extremal problem
ISSN: 0097-3165
Sayı: 6
Cilt: 114
Sayfa: 1118-1132
Sınıflandırma :
23
Erratum
Dergi Makalesi

Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Journal of Combinatorial Theory, Series A
Yayıncı:
Elsevier
Yıl :
1989
Journal of Combinatorial Theory, Series A
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Kaydet Alıntıla
DOI : 10.1016/0097-3165(89)90026-5
ISSN: 0097-3165
Sayı: 2
Cilt: 50
Sayfa: 323
Sınıflandırma :
24
From Macdonald polynomials to a charge statistic beyond type A
Dergi Makalesi

Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Journal of Combinatorial Theory, Series A
Yayıncı:
Elsevier
Yazar(lar) :
Cristian Lenart
Yıl :
2012
Journal of Combinatorial Theory, Series A
Yayıncı Web Sitesi
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Kaydet Alıntıla
The charge is an intricate statistic on words, due to Lascoux and Schützenberger, which gives positive combinatorial formulas for Lusztigʼs t-analogue of weight multiplicities and the energy function on affine crystals, both of type A. As these concepts are defined for all Lie types, it has been a long-standing problem to express them based on a generalization of charge. I present a method for addressing this problem in classical Lie types, based on the recent Ram–Yip formula for Macdonald polynomials and the quantum Bruhat order on the corresponding Weyl group. The details of the method are carried out in type A (where we recover the classical charge) and type C (where we define a new statistic).
DOI : 10.1016/j.jcta.2011.11.013
Anahtar Kelimeler : Macdonald polynomials, Alcove walks, Ramu2013Yip formula, Kashiwarau2013Nakashima columns, Charge statistic
ISSN: 0097-3165
Sayı: 3
Cilt: 119
Sayfa: 683-712
Sınıflandırma :
25
On an inverse problem of Erdős, Kleitman, and Lemke
Dergi Makalesi

Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Journal of Combinatorial Theory, Series A
Yayıncı:
Elsevier
Yazar(lar) :
Qinghai Zhong
Yıl :
2021
Journal of Combinatorial Theory, Series A
Yayıncı Web Sitesi
Tam Metin
Kaydet Alıntıla
Let (G,1G) be a finite group and let S=g1⋅…⋅gℓ be a nonempty sequence over G. We say S is a tiny product-one sequence if its terms can be ordered such that their product equals 1G and ∑i=1ℓ1ord(gi)≤1. Let ti(G) be the smallest integer t such that every sequence S over G with |S|≥t has a tiny product-one subsequence. The direct problem is to obtain the exact value of ti(G), while the inverse problem is to characterize the structure of long sequences over G which have no tiny product-one subsequence. In this paper, we consider the inverse problem for cyclic groups and we also study both direct and inverse problems for dihedral groups and dicyclic groups.
DOI : 10.1016/j.jcta.2020.105323
Anahtar Kelimeler : Product-one sequences, Zero-sum sequences, Cross number, Cyclic groups, Dihedral groups, Dicyclic groups
ISSN: 0097-3165
Cilt: 177
Sayfa: 105323
Sınıflandırma :
26
Cyclic and pseudo-cyclic MDS codes of length q + 1
Dergi Makalesi

Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Journal of Combinatorial Theory, Series A
Yayıncı:
Elsevier
Yazar(lar) :
Carsten Dahl , Jens P Pedersen
Yıl :
1992
Journal of Combinatorial Theory, Series A
Yayıncı Web Sitesi
Tam Metin
Kaydet Alıntıla
We explicitly show that cyclic and pseudo-cyclic MDS codes of length q + 1, obtained by a BCH-construction, are generalized Reed-Solomon codes.
DOI : 10.1016/0097-3165(92)90104-3
ISSN: 0097-3165
Sayı: 1
Cilt: 59
Sayfa: 130-133
Sınıflandırma :
Cebir %57
27
New bounds for partial spreads ofH(2d−1,q2)and partial ovoids of the Ree–Tits octagon
Dergi Makalesi

Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Journal of Combinatorial Theory, Series A
Yayıncı:
Elsevier
Yazar(lar) :
Ferdinand Ihringer , Peter Sin , Qing Xiang
Yıl :
2018
Journal of Combinatorial Theory, Series A
Yayıncı Web Sitesi
Tam Metin
Kaydet Alıntıla
Two results are obtained that give upper bounds on partial spreads and partial ovoids respectively. The first result is that the size of a partial spread of the Hermitian polar space H(3,q2) is at most ((2p3+p)/3)t+1, where q=pt, p is a prime. For fixed p this bound is in o(q3), which is asymptotically better than the previous best known bound of (q3+q+2)/2. Similar bounds for partial spreads of H(2d−1,q2), d even, are given. The second result is that the size of a partial ovoid of the Ree–Tits octagon O(2t) is at most 26t+1. This bound, in particular, shows that the Ree–Tits octagon O(2t) does not have an ovoid.
DOI : 10.1016/j.jcta.2017.08.003
Anahtar Kelimeler : Association scheme, Generalized n-gon, Hermitian polar space, Oppositeness graph, Ovoid, Partial ovoid, p-rank, Partial spread, Spread, The Reeu2013Tits octagon
ISSN: 0097-3165
Cilt: 153
Sayfa: 46-53
Sınıflandırma :
28
Harmonic differential forms for pseudo-reflection groups I. Semi-invariants
Dergi Makalesi

Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Journal of Combinatorial Theory, Series A
Yayıncı:
Elsevier BV
Yazar(lar) :
Joshua P. Swanson , Nolan R. Wallach
Yıl :
2021
Journal of Combinatorial Theory, Series A
Yayıncı Web Sitesi
Tam Metin
Kaydet Alıntıla
We provide a type-independent construction of an explicit basis for the semi-invariant harmonic differential forms of an arbitrary pseudo-reflection group in characteristic zero. Equivalently, we completely describe the structure of the χ-isotypic components of the corresponding super coinvariant algebras in one commuting and one anti-commuting set of variables, for all linear characters χ. In type A, we verify a specialization of a conjecture of Zabrocki [37] which provides a representation-theoretic model for the Delta conjecture of Haglund–Remmel–Wilson [10]. Our “top-down” approach uses the methods of Cartan's exterior calculus and is in some sense dual to related work of Solomon [29], Orlik–Solomon [21], and Shepler [27], [28] describing (semi-)invariant differential forms.
DOI : 10.1016/j.jcta.2021.105474
Anahtar Kelimeler : Coinvariant algebras, Pseudo-reflection groups, Harmonics, Semi-invariants, Invariant theory
ISSN: 0097-3165
Cilt: 182
Sayfa: 105474
29
Class 3 association schemes whose symmetrizations have two classes
Dergi Makalesi

Dergi Makalesi
Kaynak :
Science Direct
Dergi:
Journal of Combinatorial Theory, Series A
Yayıncı:
Elsevier
Yazar(lar) :
Sung Y Song
Yıl :
1995
Journal of Combinatorial Theory, Series A
Yayıncı Web Sitesi
Tam Metin
Kaydet Alıntıla
For a given commutative association scheme L, by fusing all the non-self-paired relations pairwise with their symmetric counterparts, we can obtain a new symmetric association scheme L̃. In this paper, we investigate when a symmetric association scheme L̃ of class 2 admits a symmetrizable commutative fission scheme L of class 3. By studying the feasible parameter sets obtained from the acceptible fission character tables of given symmetric schemes, we discover that there are infinitely many symmetric association schemes of class 2, each of which admits one or two symmetrizable commutative fission schemes of class 3. We then characterize and classify some such symmetric schemes and their symmetrizable commutative fission schemes. Also we prove that none of the Hamming schemes H(2, q) with q ≥ 3, and none of the Johnson schemes J(ν, 2) with ν ≥ 5 and ν ≢ 7(mod 8) have such commutative fission schemes of class 3. H(2, 2) has a symmetrizable commutative fission scheme which is isomorphic to the group scheme L( Z4), and J(4, 2) has one such fission scheme coming from the action of the alternating group A4 on the set of two-element subsets from a four-element set.
DOI : 10.1016/0097-3165(95)90077-2
ISSN: 0097-3165
Sayı: 1
Cilt: 70
Sayfa: 1-29
Sınıflandırma :

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