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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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

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

First available in Project Euclid: 14 December 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]

Affine semigroup gluing Frobenius vector Hilbert series


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.

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