Betti numbers of Stanley-Reisner rings determine hierarchical Markov degrees

DOI10.1007/s10801-012-0381-1zbMath1272.13019arXiv0910.1610OpenAlexW2060449355MaRDI QIDQ2376294

Sonja Petrović, Erik Stokes

Publication date: 21 June 2013

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0910.1610

zbMATH Keywords

Betti numbersMarkov basisStanley-Reisner idealMarkov widthtoric ideal generators

Mathematics Subject Classification ID

Multivariate analysis (62H99) Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Contingency tables (62H17) Combinatorial aspects of simplicial complexes (05E45)

Related Items (2)

Betti numbers of polynomial hierarchical models for experimental designs ⋮ Multigraded commutative algebra of graph decompositions

Uses Software

• Macaulay2
• 4ti2

Cites Work

• Unnamed Item
• Algebraic algorithms for sampling from conditional distributions
• Markov bases of three-way tables are arbitrarily complicated
• The largest group of invariance for Markov bases and toric ideals
• Minimal Basis for a Connected Markov Chain over 3 x 3 x K Contingency Tables with Fixed Two-Dimensional Marginals
• Using Algebraic Geometry

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