Revista Matemática Iberoamericana

Minimal Resolutions of Lattice Ideals and Integer Linear Programming

Emilio Briales, Antonio Campillo, Pilar Pisón, and Alberto Vigneron

Full-text: Open access

Abstract

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.

Article information

Source
Rev. Mat. Iberoamericana, Volume 19, Number 2 (2003), 287-306.

Dates
First available in Project Euclid: 8 September 2003

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1063050153

Mathematical Reviews number (MathSciNet)
MR2023185

Zentralblatt MATH identifier
1094.13017

Subjects
Primary: 13D02: Syzygies, resolutions, complexes 14M25: Toric varieties, Newton polyhedra [See also 52B20]
Secondary: 13P10: Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) 68W30: Symbolic computation and algebraic computation [See also 11Yxx, 12Y05, 13Pxx, 14Qxx, 16Z05, 17-08, 33F10] 90C27: Combinatorial optimization

Keywords
resolutions simplicial complex syzygy lattice ideal regularity integer linear programming Hilbert bases Gröbner bases

Citation

Briales, Emilio; Campillo, Antonio; Pisón, Pilar; Vigneron, Alberto. Minimal Resolutions of Lattice Ideals and Integer Linear Programming. Rev. Mat. Iberoamericana 19 (2003), no. 2, 287--306. https://projecteuclid.org/euclid.rmi/1063050153


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