Intersection theorems and mod \(p\) rank of inclusion matrices

DOI10.1016/0097-3165(90)90007-JzbMath0744.05008OpenAlexW2138054029MaRDI QIDQ1813781

Peter Frankl

Publication date: 25 June 1992

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0097-3165(90)90007-j

zbMATH Keywords

intersection theoremsinclusion matricesnull \(t\)-designs

Mathematics Subject Classification ID

Partitions of sets (05A18) Combinatorial aspects of block designs (05B05) Combinatorial aspects of matrices (incidence, Hadamard, etc.) (05B20) Extremal set theory (05D05)

Related Items (29)

The Smith group of the hypercube graph ⋮ Intersection Matrices Revisited ⋮ Shift graphs and lower bounds on Ramsey numbers \(r_ k(l;r)\) ⋮ On the bases of trades ⋮ A note on linear Sperner families ⋮ On the rank of higher inclusion matrices ⋮ Order shattering and Wilson's theorem ⋮ Inclusion matrices for rainbow subsets ⋮ Standard monomials for \(q\)-uniform families and a conjecture of Babai and Frankl ⋮ Smith normal forms of incidence matrices ⋮ Rank of inclusion matrices and modular representation theory ⋮ Inclusion matrices and chains ⋮ Extending small arcs to large arcs ⋮ Quasi-random subsets of \(\mathbb{Z}_ n\) ⋮ Some Combinatorial Applications of Gröbner Bases ⋮ On hypergraphs having evenly distributed subhypergraphs ⋮ The \(k\)-orbit reconstruction and the orbit algebra ⋮ On mod-\(p\) Alon-Babai-Suzuki inequality ⋮ On modular homology of simplicial complexes: Shellability ⋮ A new proof of a classical theorem in design theory ⋮ Saturated simplicial complexes ⋮ Resilience of ranks of higher inclusion matrices ⋮ Inclusion matrices and the MDS conjecture ⋮ Cohomological Aspects of Hypergraphs ⋮ On 1-factorizations of bipartite Kneser graphs ⋮ Some properties of a higher-order coboundary operator ⋮ Moore-Penrose inverse of set inclusion matrices ⋮ A homological interpretation of certain incidence matrices \(\text{mod }p\) ⋮ Gröbner bases for complete uniform families

Cites Work

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• A short proof of the nonuniform Ray-Chaudhuri-Wilson inequality
• Intersection theorems with geometric consequences
• Multilinear polynomials and Frankl-Ray-Chaudhuri-Wilson type intersection theorems
• On t-designs
• On incidence matrices of finite projective and affine spaces
• The module structure of integral designs
• On the Structure oft-Designs
• Incidence Matrices of Subsets—A Rank Formula

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