Details:
Title  Universal Gr\"obner bases of colored partition identities.  Author(s)  T. Bogart, Raymond Hemmecke, Sonja Petrovic  Type  Article in Journal  Abstract  Associated to any toric ideal are two special generating sets: the universal Gröbner basis and the Graver basis, which encode polyhedral and combinatorial properties of the ideal, or equivalently, its defining matrix. If the two sets coincide, then the complexity of the Graver bases of the higher Lawrence liftings of the toric matrices is bounded. While a general classification of all matrices for which both sets agree is far from known, we identify all such matrices within two families of nonunimodular matrices, namely, those defining rational normal scrolls and those encoding homogeneous primitive colored partition identities. This also allows us to show that higher Lawrence liftings of matrices with fixed Gröbner and Graver complexities do not preserve equality of the two bases. The proof of our classification combines computations with the theoretical tool of Graver complexity of a pair of matrices.  Keywords  Graver bases, Universal Gröbner bases, partition identities, colored partitions, rational normal scrolls, state polytope, toric ideal  ISSN  10586458; 1944950X/e 
URL 
http://www.tandfonline.com/doi/abs/10.1080/10586458.2012.703886 
Language  English  Journal  Exp. Math.  Volume  21  Number  4  Pages  395401  Publisher  Taylor & Francis, Philadelphia, PA  Year  2012  Edition  0  Translation 
No  Refereed 
No 
