Some Combinatorial Applications of Gröbner Bases

DOI10.1007/978-3-642-21493-6_4zbMath1307.05236OpenAlexW1546490581MaRDI QIDQ3014931

Tamás Mészáros, Lajos Rónyai

Publication date: 8 July 2011

Published in: Algebraic Informatics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-21493-6_4

zbMATH Keywords

lexicographic orderGröbner basisinclusion matrixHilbert functionstandard monomialcombinatorial Nullstellensatzvanishing idealrank formula\(S\)-extremal set family

Mathematics Subject Classification ID

Extremal set theory (05D05) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Polynomials in real and complex fields: location of zeros (algebraic theorems) (12D10) Combinatorial aspects of commutative algebra (05E40)

Related Items (10)

A uniform version of a theorem by Dvir and Moran ⋮ What convex geometries tell about shattering-extremal systems ⋮ Two results about the hypercube ⋮ Shattering, graph orientations, and connectivity ⋮ Standard monomials and extremal vector systems ⋮ On partial cubes, well-graded families and their duals with some applications in graphs ⋮ Shattering-extremal set systems of VC dimension at most 2 ⋮ Polynomial criterion for abelian difference sets ⋮ Standard monomials and extremal point sets ⋮ Shattering-extremal set systems from Sperner families

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