# 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.

# Presentations

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

# Bibtex

```
@article{SanDiegoPaper,
title={Augmented Hilbert series of numerical semigroups},
url={http://math.colgate.edu/~integers/t32/t32.pdf},
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.},
journal={Integers},
author={Glenn, Jeske and O'Neill, Christopher and Ponomarenko, Vadim and Sepanski, Benjamin},
year={2019},
number= {32},
month={Jun} ,
pages ={1--15},
}
```