Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 51, No. 1, pp. 4556 (2010) 

Neighborliness of marginal polytopesThomas KahleMax Planck Institute for Mathematics in the Sciences, Inselstrasse 22, D04103 Leipzig, Germany, email: kahle@mis.mpg.deAbstract: A neighborliness property of marginal polytopes of hierarchical models, depending on the cardinality of the smallest nonface of the underlying simplicial complex, is shown. The case of binary variables is studied explicitly, then the general case is reduced to the binary case. A Markov basis for binary hierarchical models whose simplicial complexes is the complement of an interval is given. Keywords: marginal polytopes, Markov bases, hierarchical models Classification (MSC2000): 52B05, 60C05 Full text of the article:
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