Toric Ideals Arising from Contingency Tables

Fundamental questions on semigroup rings and toric ideals arising from contingency tables will be studied. In addition to discussing recent developments on such the topic, the algebraic background of contingency tables and basic notions related with Grbases will be also explained clearly.

[1]  Takayuki Hibi,et al.  Toric Ideals Generated by Quadratic Binomials , 1999 .

[2]  A. Takemura,et al.  Minimal Basis for a Connected Markov Chain over 3 × 3 ×K Contingency Tables with Fixed Two‐Dimensional Marginals , 2003 .

[3]  B. Sturmfels.  Gröbner bases and convex polytopes , 1995 .

[4]  Takayuki Hibi,et al.  INDISPENSABLE BINOMIALS OF FINITE GRAPHS , 2005 .

[5]  Bernd Sturmfels,et al.  Higher Lawrence configurations , 2003, J. Comb. Theory, Ser. A.

[6]  Seth Sullivant.  Compressed polytopes and statistical disclosure limitation , 2004 .

[7]  A. Takemura,et al.  Some characterizations of minimal Markov basis for sampling from discrete conditional distributions , 2004 .

[8]  P. Diaconis,et al.  Algebraic algorithms for sampling from conditional distributions , 1998 .

[9]  Takayuki Hibi,et al.  Combinatorial pure subrings , 2000 .

[10]  Seth Sullivant,et al.  Gröbner Bases and Polyhedral Geometry of Reducible and Cyclic Models , 2002, J. Comb. Theory, Ser. A.

[11]  Takayuki Hibi,et al.  A Normal (0, 1)-Polytope None of Whose Regular Triangulations Is Unimodular , 1999, Discret. Comput. Geom..

[12]  T. Hibi,et al.  Convex polytopes all of whose reverse lexicographic initial ideals are squarefree , 2001 .

[13]  D. R. Fulkerson,et al.  Some Properties of Graphs with Multiple Edges , 1965, Canadian Journal of Mathematics.

[14]  A. Agresti,et al.  Categorical Data Analysis , 1991, International Encyclopedia of Statistical Science.

[15]  Takayuki Hibi,et al.  Compressed polytopes, initial ideals and complete multipartite graphs , 2000 .