Exploiting Symmetries in the Computation of Graver Bases

2004/10/14 by Raymond Hemmecke, Hemmecke, Raymond
Computer Science · Mathematics · #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Tensor decomposition and applications #math.CO

paper · pdf · doi:10.48550/arxiv.math/0410334

arxiv created 2004/10/14 · openalex publication_date 2004/10/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Many challenging Graver bases computations, like for multi-way tables in statistics, have a highly symmetric problem structure that is not exploited so far computationally. In this paper we present a Graver basis algorithm for sublattices of \Zⁿ that exploits existing symmetry.

Citations

• Test Sets for Integer Programs with Z-Convex Objective
• Algebraic algorithms for sampling from conditional distributions

Related

• Notes on Symmetric Bases
• Notes on "Symmetric Bases with large 2-range"
• Some new symmetric structures in Ramsey theory
• Mixed radix numeration bases: Horner's rule, Yang-Baxter equation and Furstenberg's conjecture
• Graver Bases and Universal Gröbner Bases for Linear Codes