Journal of Commutative Algebra

Frobenius vectors, Hilbert series and gluings of affine semigroups

A. Assi, P.A. García-Sánchez, and I. Ojeda

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Abstract

Let $S_1$ and $S_2$ be two affine semigroups, and let $S$ be the gluing of $S_1$ and $S_2$. Several invariants of $S$ are related to those of $S_1$ and $S_2$; we review some of the most important properties preserved under gluings. The aim of this paper is to prove that this is the case for the Frobenius vector and the Hilbert series. Applications to complete intersection affine semigroups are also given.

Article information

Source
J. Commut. Algebra, Volume 7, Number 3 (2015), 317-335.

Dates
First available in Project Euclid: 14 December 2015

Permanent link to this document
https://projecteuclid.org/euclid.jca/1450102157

Digital Object Identifier
doi:10.1216/JCA-2015-7-3-317

Mathematical Reviews number (MathSciNet)
MR3433984

Zentralblatt MATH identifier
1350.20043

Subjects
Primary: 20M14: Commutative semigroups
Secondary: 05A15: Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx] 11D07: The Frobenius problem 14M10: Complete intersections [See also 13C40]

Keywords
Affine semigroup gluing Frobenius vector Hilbert series

Citation

Assi, A.; García-Sánchez, P.A.; Ojeda, I. Frobenius vectors, Hilbert series and gluings of affine semigroups. J. Commut. Algebra 7 (2015), no. 3, 317--335. doi:10.1216/JCA-2015-7-3-317. https://projecteuclid.org/euclid.jca/1450102157


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