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Degree and algebraic properties of lattice and matrix ideals

Author
O'Carroll, L.; Planas-Vilanova, F. A.; Villarreal, R.
Type of activity
Journal article
Journal
SIAM journal on discrete mathematics
Date of publication
2014-01-01
Volume
28
Number
1
First page
394
Last page
427
DOI
https://doi.org/10.1137/130922094 Open in new window
Repository
http://hdl.handle.net/2117/23006 Open in new window
URL
http://epubs.siam.org/doi/abs/10.1137/130922094 Open in new window
Abstract
We study the degree of nonhomogeneous lattice ideals over arbitrary fields, and give formulas to compute the degree in terms of the torsion of certain factor groups of Z(s) and in terms of relative volumes of lattice polytopes. We also study primary decompositions of lattice ideals over an arbitrary field using the Eisenbud-Sturmfels theory of binomial ideals over algebraically closed fields. We then use these results to study certain families of integer matrices (positive critical binomial (PCB...
Citation
O'Carroll, L.; Planas, F. A.; Villarreal, R. Degree and algebraic properties of lattice and matrix ideals. "SIAM journal on discrete mathematics", 01 Gener 2014, vol. 28, núm. 1, p. 394-427.
Keywords
BINOMIAL IDEALS, GRAPHS, PCB ideal, degree, graded binomial ideal, lattice ideal, primary decomposition
Group of research
GEOMVAP - Geometry of Manifolds and Applications

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