Augmented Hilbert series of numerical semigroups

Published in Integers, 2019

Glenn, Jeske and O'Neill Christopher and Ponomarenko, Vadim and Sepanski, Benjamin (June 3, 2019). "Augmented Hilbert series of numerical semigroups." Integers 19 #A32.

Several new explicit formulas for certain augmented Hilbert Series measuring maximal and minimal factorization lengths for all numerical semigroups.

Download paper here as published in Volume 19 of Integers.


I presented this research in a talk at the 2018 Joint Mathematics Meetings.


 title={Augmented Hilbert series of numerical semigroups},
 abstractNote={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.},
 author={Glenn, Jeske and O'Neill, Christopher and Ponomarenko, Vadim and Sepanski, Benjamin},
 number= {32},
 month={Jun} ,
 pages ={1--15},