Hamming polynomial of a demimatroid

DOI10.1007/s40863-022-00339-3zbMath1518.05036arXiv1907.09644OpenAlexW2963773447WikidataQ121631167 ScholiaQ121631167MaRDI QIDQ6171840

José Martínez-Bernal, Rafael H. Villarreal, Miguel A. Valencia-Bucio

Publication date: 18 July 2023

Published in: São Paulo Journal of Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.09644

zbMATH Keywords

simplicial complexmatroidsTutte polynomialweight enumeratorsBetti numbershigher weightsStanley-ReisnerWei dualitydemimatroidsHochster formula

Mathematics Subject Classification ID

Graph polynomials (05C31) Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) (52B40) Linear codes (general theory) (94B05) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Geometric methods (including applications of algebraic geometry) applied to coding theory (94B27) Combinatorial aspects of matroids and geometric lattices (05B35) Combinatorial aspects of simplicial complexes (05E45)

Cites Work

• Wei-type duality theorems for matroids
• A generalization of weight polynomials to matroids
• Hamming weights and Betti numbers of Stanley-Reisner rings associated to matroids
• On Brylawski's generalized duality
• Generalized Hamming weights for linear codes
• Fundamentals of Error-Correcting Codes
• Combinatorial Commutative Algebra
• Monomial Algebras
• From weight enumerators to zeta functions
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