Theory of linear and integer programming
Theory of linear and integer programming
A geometric Buchberger algorithm for integer programming
Mathematics of Operations Research
Note: A note on the problem of reporting maximal cliques
Theoretical Computer Science
Computing generating sets of lattice ideals and Markov bases of lattices
Journal of Symbolic Computation
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A binomial ideal is an ideal of the polynomial ring which is generated by binomials. In a previous paper, we gave a correspondence between pure saturated binomial ideals of K[x"1,...,x"n] and submodules of Z^n and we showed that it is possible to construct a theory of Grobner bases for submodules of Z^n. As a consequence, it is possible to follow alternative strategies for the computation of Grobner bases of submodules of Z^n (and hence of binomial ideals) which avoid the use of Buchberger algorithm. In the present paper, we show that a Grobner basis of a Z-module M@?Z^n of rank m lies into a finite set of cones of Z^m which cover a half-space of Z^m. More precisely, in each of these cones C, we can find a suitable subset Y(C) which has the structure of a finite abelian group and such that a Grobner basis of the module M (and hence of the pure saturated binomial ideal represented by M) is described using the elements of the groups Y(C) together with the generators of the cones.