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The set of all group relaxations of an integer program contains certain special members called Gomory relaxations. A family of integer programs with a fixed coefficient matrix and cost vector but varying right hand sides is a Gomory family if every program in the family can be solved by one of its Gomory relax-ations. In this paper, we characterize Gomory(More)
The purpose of this exposition 1 is to give a simple treatment of Knutson and Tao's recent proof of the saturation conjecture [10]. A finite dimensional irreducible polynomial representation of GL n (C) is determined by its highest weight, which is a weakly decreasing sequence of n non-negative integers, also called a partition [5, §8]. The irreducible(More)
Given a model in algebraic statistics and data, the likelihood function is a rational function on a projective variety. Algebraic algorithms are presented for computing all critical points of this function, with the aim of identifying the local maxima in the probability simplex. Applications include models specified by rank conditions on matrices and the(More)
This article studies the polyhedral structure and combinatorics of polytopes that arise from hierarchical models in statistics, and shows how to construct Gröbner bases of toric ideals associated to a subset of such models. We study the polytopes for cyclic models, and we give a complete polyhedral description of these polytopes in the binary cyclic case.(More)
We show that the complexity of the Markov bases of multidimensional tables stabilizes eventually if a single table dimension is allowed to vary. In particular, if this table dimension is beyond a computable bound, the Markov bases consist of elements of Markov bases of smaller tables. We give an explicit formula for this bound in terms of Graver bases. We(More)