Higher Lawrence configurations

2002/09/30 by Francisco Santos, Bernd Sturmfels · 3 citations
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Commutative Algebra and Its Applications #Polynomial and algebraic computation #math.AC #math.CO #msc:13P10 #msc:52B20 #msc:62H17

paper · pdf · doi:10.1016/s0097-3165(03)00092-x

published as J. Combin. Theory, Ser. A. 103:1 (2003), 151-164. · 12 pages. Changes from v1 and v2: minor edits. This version is to appear in the Journal of Combinatorial Theory, Ser. A

arxiv created 2003/03/31 · openalex publication_date 2003/06/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Any configuration of lattice vectors gives rise to a hierarchy of higher-dimensional configurations which generalize the Lawrence construction in geometric combinatorics. We prove finiteness results for the Markov bases, Graver bases and face posets of these configurations, and we discuss applications to the statistical theory of log-linear models.

Citations

• Algebraic algorithms for sampling from conditional distributions

Cited by

• Non-asymptotic goodness-of-fit tests and model selection in valued stochastic blockmodels
• Nonlinear Integer Programming
• A Kruskal–Katona type result and applications

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