Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 07/2017, Volume 125, pp. 168 - 177

The Ramsey number rk(s,n) is the minimum N such that every red–blue coloring of the k-subsets of {1,…,N} contains a red set of size s or a blue set of size n,...

Ordered hypergraphs | Ramsey theory | Tight-paths | MATHEMATICS | ERDOS | Cytokinins | Statistics

Ordered hypergraphs | Ramsey theory | Tight-paths | MATHEMATICS | ERDOS | Cytokinins | Statistics

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 9/2017, Volume 46, Issue 2, pp. 475 - 497

A factorization of the complete k-hypergraph $$(V,V^{\{k\}})$$ ( V , V { k } ) of index $$s\ge 2$$ s ≥ 2 , simply a (k, s) factorization on V, is a partition...

05C65 | Symmetric factorization | k -Homogeneous permutation group | Mathematics | 05C70 | 1-Factorization | 20B25 | Uniform hypergraph | Convex and Discrete Geometry | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Steiner system | 05E18 | Combinatorics | Computer Science, general | Mathieu group | Fractional linear mapping | k-Homogeneous permutation group | MATHEMATICS | COMPLETE GRAPHS

05C65 | Symmetric factorization | k -Homogeneous permutation group | Mathematics | 05C70 | 1-Factorization | 20B25 | Uniform hypergraph | Convex and Discrete Geometry | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Steiner system | 05E18 | Combinatorics | Computer Science, general | Mathieu group | Fractional linear mapping | k-Homogeneous permutation group | MATHEMATICS | COMPLETE GRAPHS

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 2/2014, Volume 39, Issue 1, pp. 187 - 208

The edges of any hypergraph parametrize a monomial algebra called the edge subring of the hypergraph. We study presentation ideals of these edge subrings, and...

Hypergraph | Markov basis | Edge ring | Mathematics | Combinatorial discrepancy | Parameter hypergraph | Monomial walk | Toric ideal | Convex and Discrete Geometry | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | Sunflower | MATHEMATICS | EDGE IDEALS | MODEL | GRAPHS | Analysis | Algebra

Hypergraph | Markov basis | Edge ring | Mathematics | Combinatorial discrepancy | Parameter hypergraph | Monomial walk | Toric ideal | Convex and Discrete Geometry | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | Sunflower | MATHEMATICS | EDGE IDEALS | MODEL | GRAPHS | Analysis | Algebra

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 5/2016, Volume 43, Issue 3, pp. 715 - 734

We determine all finite primitive groups that are automorphism groups of edge-transitive hypergraphs. This gives an answer to a problem proposed by Babai and...

20H30 | Uniform hypergraph | Convex and Discrete Geometry | Edge-transitive | Automorphism group of set systems | Mathematics | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | Primitive group | 20B15 | OVERGROUPS | MATHEMATICS | SET | NO REGULAR ORBITS | PERMUTATION-GROUPS | SUBSETS

20H30 | Uniform hypergraph | Convex and Discrete Geometry | Edge-transitive | Automorphism group of set systems | Mathematics | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | Primitive group | 20B15 | OVERGROUPS | MATHEMATICS | SET | NO REGULAR ORBITS | PERMUTATION-GROUPS | SUBSETS

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 4/2008, Volume 27, Issue 2, pp. 215 - 245

We use the correspondence between hypergraphs and their associated edge ideals to study the minimal graded free resolution of squarefree monomial ideals. The...

Graded resolutions | Convex and Discrete Geometry | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Monomial ideals | Computer Science, general | Combinatorics | Hypergraphs | Regularity | Chordal graphs | MATHEMATICS | hypergraphs | graded resolutions | RESOLUTIONS | chordal graphs | regularity | monomial ideals

Graded resolutions | Convex and Discrete Geometry | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | Monomial ideals | Computer Science, general | Combinatorics | Hypergraphs | Regularity | Chordal graphs | MATHEMATICS | hypergraphs | graded resolutions | RESOLUTIONS | chordal graphs | regularity | monomial ideals

Journal Article

6.
Full Text
Connection Between Polynomial Optimization and Maximum Cliques of Non-Uniform Hypergraphs

Order, ISSN 0167-8094, 7/2018, Volume 35, Issue 2, pp. 301 - 319

In Motzkin and Straus (Canad. J. Math 498 17, 533540 1965) provided a connection between the order of a maximum clique in a graph G and the Lagrangian function...

Algebra | Polynomial optimization | Maximum clique | Mathematics | Order, Lattices, Ordered Algebraic Structures | Turán density | Discrete Mathematics | MOTZKIN-STRAUS THEOREM | MATHEMATICS | Turan density | LAGRANGIANS | TURAN

Algebra | Polynomial optimization | Maximum clique | Mathematics | Order, Lattices, Ordered Algebraic Structures | Turán density | Discrete Mathematics | MOTZKIN-STRAUS THEOREM | MATHEMATICS | Turan density | LAGRANGIANS | TURAN

Journal Article

1974, Lecture Notes in Mathematics, ISBN 9783540068464, Volume 411, XII, 292

eBook

Journal of Algebraic Combinatorics, ISSN 0925-9899, 2/2007, Volume 25, Issue 1, pp. 101 - 110

Let $${\cal F}$$ be a k-uniform hypergraph on [n] where k−1 is a power of some prime p and n≥ n 0(k). Our main result says that if $$|F|> ({n\atop k-1})...

Trace | Hypergraph | Convex and Discrete Geometry | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | VC-dimension | Extremal problems | Computer Science, general | Combinatorics | MATHEMATICS | ORDER | trace | hypergraph | extremal problems | INTERSECTION-THEOREMS | SETS | Computer science | Venture capital

Trace | Hypergraph | Convex and Discrete Geometry | Mathematics | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | VC-dimension | Extremal problems | Computer Science, general | Combinatorics | MATHEMATICS | ORDER | trace | hypergraph | extremal problems | INTERSECTION-THEOREMS | SETS | Computer science | Venture capital

Journal Article

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, ISSN 1364-5021, 04/2019, Volume 475, Issue 2224, p. 20180581

For more than 150 years, the structure of the periodic system of the chemical elements has intensively motivated research in different areas of chemistry and...

TABLE | polarizability | POSETS | covalent bonds | mathematics | similarity | MULTIDISCIPLINARY SCIENCES | ordered hypergraph | CHEMISTRY | periodic system | RANKING | CHEMICAL-ELEMENTS | Computer Science - Discrete Mathematics | 1008 | covalentbonds | 1002 | 108

TABLE | polarizability | POSETS | covalent bonds | mathematics | similarity | MULTIDISCIPLINARY SCIENCES | ordered hypergraph | CHEMISTRY | periodic system | RANKING | CHEMICAL-ELEMENTS | Computer Science - Discrete Mathematics | 1008 | covalentbonds | 1002 | 108

Journal Article

Discrete Mathematics, ISSN 0012-365X, 02/2016, Volume 339, Issue 2, pp. 499 - 505

For a k-uniform hypergraph G with vertex set {1,…,n}, the ordered Ramsey number ORt(G) is the least integer N such that every t-coloring of the edges of the...

Ordered Ramsey numbers | Matchings | 05C55 | Loose paths | Hypergraph Ramsey theory | MATHEMATICS

Ordered Ramsey numbers | Matchings | 05C55 | Loose paths | Hypergraph Ramsey theory | MATHEMATICS

Journal Article

Kongzhi yu Juece/Control and Decision, ISSN 1001-0920, 04/2017, Volume 32, Issue 4, pp. 637 - 641

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 6/2019, Volume 49, Issue 4, pp. 461 - 473

Restrictions of incidence preserving path maps produce oriented hypergraphic All Minors Matrix-tree Theorems for Laplacian and adjacency matrices. The images...

05C65 | 05C22 | 05C50 | Bidirected graph | Mathematics | Signed graph | Matrix-tree theorem | Convex and Discrete Geometry | Oriented hypergraph | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Laplacian matrix | Combinatorics | Computer Science, general

05C65 | 05C22 | 05C50 | Bidirected graph | Mathematics | Signed graph | Matrix-tree theorem | Convex and Discrete Geometry | Oriented hypergraph | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Laplacian matrix | Combinatorics | Computer Science, general

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 12/2016, Volume 44, Issue 4, pp. 875 - 904

Given a squarefree monomial ideal $$I \subseteq R =k[x_1,\ldots ,x_n]$$ I ⊆ R = k [ x 1 , … , x n ] , we show that $$\widehat{\alpha }(I)$$ α ^ ( I ) , the...

Secondary 13A02 | Primary 13F20 | Linear programming | Mathematics | Waldschmidt constant | Fractional chromatic number | Convex and Discrete Geometry | Graphs | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Monomial ideals | Symbolic powers | 14N05 | Combinatorics | Computer Science, general | Hypergraphs | Resurgence | RESURGENCES | X P-1 | MATHEMATICS | LINEAR-SUBSPACES | POINTS

Secondary 13A02 | Primary 13F20 | Linear programming | Mathematics | Waldschmidt constant | Fractional chromatic number | Convex and Discrete Geometry | Graphs | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Monomial ideals | Symbolic powers | 14N05 | Combinatorics | Computer Science, general | Hypergraphs | Resurgence | RESURGENCES | X P-1 | MATHEMATICS | LINEAR-SUBSPACES | POINTS

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 2/2014, Volume 39, Issue 1, pp. 99 - 125

A family of polytopes introduced by E.M. Feichtner, A. Postnikov, and B. Sturmfels, which were named nestohedra, consists in each dimension of an interval of...

Hypergraph | Simplex | Combinatorial blowup | Simple polytope | Stellar subdivision | Mathematics | Cyclohedron | Truncation | Building set | Permutohedron | Convex and Discrete Geometry | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | Nested set | Associahedron | MATHEMATICS

Hypergraph | Simplex | Combinatorial blowup | Simple polytope | Stellar subdivision | Mathematics | Cyclohedron | Truncation | Building set | Permutohedron | Convex and Discrete Geometry | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | Nested set | Associahedron | MATHEMATICS

Journal Article

Order, ISSN 0167-8094, 11/2018, Volume 35, Issue 3, pp. 557 - 579

We present a refinement of Ramsey numbers by considering graphs with a partial ordering on their vertices. This is a natural extension of the ordered Ramsey...

Algebra | Partially-ordered sets | Ordered Ramsey numbers | Ordered graphs | Mathematics | Order, Lattices, Ordered Algebraic Structures | Ramsey theory | Discrete Mathematics | MATHEMATICS | POSET-FREE FAMILIES | THEOREM | HYPERGRAPHS | SUBSETS | PATHS | SUBPOSET

Algebra | Partially-ordered sets | Ordered Ramsey numbers | Ordered graphs | Mathematics | Order, Lattices, Ordered Algebraic Structures | Ramsey theory | Discrete Mathematics | MATHEMATICS | POSET-FREE FAMILIES | THEOREM | HYPERGRAPHS | SUBSETS | PATHS | SUBPOSET

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 5/2018, Volume 47, Issue 3, pp. 441 - 472

We explore connections between the generalized multiplicities of square-free monomial ideals and the combinatorial structure of the underlying hypergraphs...

Co-convex bodies | 13H15 | 52B20 | Edge polytopes | Mathematics | j -multiplicity | upvarepsilon $$ ε -multiplicity | Volumes | 13D40 | Convex and Discrete Geometry | Newton polyhedra | Free sums | Edge ideals | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | Hypergraphs | ε -multiplicity | j-multiplicity | TORIC IDEALS | MATHEMATICS | ANALYTIC SPREAD | epsilon-multiplicity | Algebra

Co-convex bodies | 13H15 | 52B20 | Edge polytopes | Mathematics | j -multiplicity | upvarepsilon $$ ε -multiplicity | Volumes | 13D40 | Convex and Discrete Geometry | Newton polyhedra | Free sums | Edge ideals | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | Hypergraphs | ε -multiplicity | j-multiplicity | TORIC IDEALS | MATHEMATICS | ANALYTIC SPREAD | epsilon-multiplicity | Algebra

Journal Article

Electronic Journal of Combinatorics, ISSN 1077-8926, 04/2012, Volume 19, Issue 2, pp. 1 - 17

We study $r$-differential posets, a class of combinatorial objects introduced in 1988 by the first author, which gathers together a number of remarkable...

Hasse walk | Hypergraph | Rank function | Partially ordered set | Young-fibonacci lattice | Hasse diagram | Interval conjecture | Finite projective plane | Young lattice | Steiner system | Differential poset

Hasse walk | Hypergraph | Rank function | Partially ordered set | Young-fibonacci lattice | Hasse diagram | Interval conjecture | Finite projective plane | Young lattice | Steiner system | Differential poset

Journal Article

SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2008, Volume 23, Issue 1, pp. 487 - 510

Let P = P-1 x ... x P-n be the product of n partially ordered sets (posets). Given a subset A. P, we consider problem DUAL(P, A, B) of extending a given...

Forests | Duality testing | Monotone properties | Infrequent elements | Lattices | Monotone generation | Ordered sets | Enumeration algorithms | Hypergraph transversals | duality testing | MATHEMATICS, APPLIED | monotone generation | ordered sets | enumeration algorithms | monotone properties | infrequent elements | lattices | forests | hypergraph transversals

Forests | Duality testing | Monotone properties | Infrequent elements | Lattices | Monotone generation | Ordered sets | Enumeration algorithms | Hypergraph transversals | duality testing | MATHEMATICS, APPLIED | monotone generation | ordered sets | enumeration algorithms | monotone properties | infrequent elements | lattices | forests | hypergraph transversals

Journal Article

Advances in Applied Mathematics, ISSN 0196-8858, 2007, Volume 38, Issue 2, pp. 258 - 266

We present two extensions of the linear bound, due to Marcus and Tardos, on the number of 1-entries in an n × n ( 0 , 1 ) -matrix avoiding a fixed permutation...

Stanley–Wilf conjecture | Ordered hypergraph | [formula omitted]-Matrix | Extremal theory | Stanley-Wilf conjecture | (0, 1)-Matrix | extremal theory | MATHEMATICS, APPLIED | (0.1)-matrix | MATRICES | ordered hypergraph | PARTITIONS

Stanley–Wilf conjecture | Ordered hypergraph | [formula omitted]-Matrix | Extremal theory | Stanley-Wilf conjecture | (0, 1)-Matrix | extremal theory | MATHEMATICS, APPLIED | (0.1)-matrix | MATRICES | ordered hypergraph | PARTITIONS

Journal Article

Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 1992, Volume 56, Issue 2, pp. 278 - 295

The dimension D( S) of a family S of subsets of n = {1, 2, …, n} is defined as the minimum number of permutations of n such that every A ∈ S is an intersection...

MATHEMATICS | PARTIALLY ORDERED SETS | GRAPHS

MATHEMATICS | PARTIALLY ORDERED SETS | GRAPHS

Journal Article

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