Revista Matemática Iberoamericana


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Volume 19, Issue 2, 2003, pp. 287–306
DOI: 10.4171/RMI/347

Published online: 2003-08-31

Minimal Resolutions of Lattice Ideals and Integer Linear Programming

Emilio Briales-Morales[1], Antonio Campillo-López[2], Pilar Pisón-Casares[3] and Alberto Vigneron-Tenorio[4]

(1) Universidad de Sevilla, Spain
(2) Universidad de Valladolid, Spain
(3) Universidad de Sevilla, Spain
(4) Universidad de Cádiz, Jerez de la Frontera, Spain

A combinatorial description of the minimal free resolution of a lattice ideal allows us to the connection of Integer Linear Programming and Algebra. 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.

Keywords: Resolutions, simplicial complex, syzygy, lattice ideal, regularity, Integer Linear Programming, Hilbert bases, Gröbner bases

Briales-Morales Emilio, Campillo-López Antonio, Pisón-Casares Pilar, Vigneron-Tenorio Alberto: Minimal Resolutions of Lattice Ideals and Integer Linear Programming. Rev. Mat. Iberoamericana 19 (2003), 287-306. doi: 10.4171/RMI/347