Higher Lawrence configurations

2002/09/30 by Francisco Santos, Bernd Sturmfels · 1 citation
Mathematics · #math.CO #math.AC #msc:52B20 #msc:13P10 #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 · arxiv updated 2009/11/30

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.

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