The Degree and Regularity of Vanishing Ideals of Algebraic Toric Sets Over Finite Fields

DOI10.1080/00927872.2012.686643zbMath1286.13022arXiv1110.2124OpenAlexW2009550926MaRDI QIDQ2848509

Maria Vaz Pinto, Rafael H. Villarreal

Publication date: 26 September 2013

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.2124

zbMATH Keywords

bipartite graphcomplete intersectiondegreecluttervanishing idealevaluation codealgebraic toric set

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Combinatorial codes (94B25)

Related Items

Parameterized codes associated to the edges of some subgraphs of a simple graph ⋮ Joins, ears and Castelnuovo-Mumford regularity ⋮ Generalized Hamming weights and some parameterized codes ⋮ Parameterized codes over graphs ⋮ Regularity of the vanishing ideal over a parallel composition of paths ⋮ Regularity and algebraic properties of certain lattice ideals ⋮ Regularity of the vanishing ideal over a bipartite nested ear decomposition ⋮ Vanishing Ideals Over Graphs and Even Cycles ⋮ Degree and regularity of Eulerian ideals of hypergraphs

Uses Software

• Macaulay2
• SINGULAR

Cites Work

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• Vanishing Ideals Over Graphs and Even Cycles
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