Augmented Hilbert series of numerical semigroups

Abstract

A numerical semigroup $S$ is a subset of the non-negative integers containing $0$ that is closed under addition. The Hilbert series of $S$ (a formal power series equal to the sum of terms $t^n$ over all $n\in S$) can be expressed as a rational function in $t$ whose numerator is characterized in terms of the topology of a simplicial complex determined by membership in $S$. In this paper, we obtain analogous rational expressions for the related power series whose coefficient of $t^n$ equals $f(n)$ for one of several semigroup-theoretic invariants $f:S\to \mathbb{R}$ known to be eventually quasipolynomial.

References in corpus (7)

• Sparse solutions of linear Diophantine equations
• On dynamic algorithms for factorization invariants in numerical monoids
• Simplicial complexes and minimal free resolution of monomial algebras
• On factorization invariants and Hilbert functions
• On the Linearity of ω-primality in Numerical Monoids
• How Do You Measure Primality?
• Factorization invariants in numerical monoids