MULTIVALUED GENERALIZATIONS OF THE FRANKL–PACH THEOREM

DOI10.1142/S0219498811005282zbMath1241.13024arXiv1008.4660OpenAlexW2963114004MaRDI QIDQ5389512

Lajos Rónyai, Gábor Hegedüs

Publication date: 21 April 2012

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1008.4660

zbMATH Keywords

Gröbner basisstandard monomialshattered setuniform family\(n\)-tuple system

Mathematics Subject Classification ID

Extremal set theory (05D05) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) (13P25) Combinatorial aspects of commutative algebra (05E40)

Cites Work

• On disjointly representable sets
• On the VC-dimension of uniform hypergraphs
• On the density of sets of vectors
• A forbidden configuration theorem of Alon
• Existence of submatrices with all possible columns
• Coordinate density of sets of vectors
• Shattering news
• Traces of antichains
• Gröbner bases for complete uniform families
• A generalization of Sauer's lemma
• The lex game and some applications
• A combinatorial problem; stability and order for models and theories in infinitary languages
• On the density of families of sets
• On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities
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