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Combinatoric of syzygies for semigroup algebras.

Emilio Briales;  Pilar Pisón;  Antonio Campillo;  Carlos Marijuán — 1998

Collectanea Mathematica

We describe how the graded minimal resolution of certain semigroup algebras is related to the combinatorics of some simplicial complexes. We obtain characterizations of the Cohen-Macaulay and Gorenstein conditions. The Cohen-Macaulay type is computed from combinatorics. As an application, we compute explicitly the graded minimal resolution of monomial both affine and simplicial projective surfaces.

Minimal resolutions of lattice ideals and integer linear programming.

Emilio Briales-Morales;  Antonio Campillo-López;  Pilar Pisón-Casares;  Alberto Vigneron-Tenorio — 2003

Revista Matemática Iberoamericana

A combinatorial description of the minimal free resolution of a lattice ideal allows us to the connection of Integer Linear Programming and Al1gebra. The non null reduced homology spaces of some simplicial complexes are the key. The extremal rays of the associated cone reduce the number of variables.

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