Presented at the AMS-MAA-SIAM Special Session on Undergraduate Research at the 2018 Joint Mathematics Meetings in San Diego, California, funded by an MAA Travel Grant for Undergraduates. This was joint work with Christopher O’Neill, Jeske Glenn, and Vadim Ponomarenko from the 2017 SDSU REU, presenting new explicit formulas for augmented Hilbert series that measure factorization lengths in numerical semigroups. A weighted Euler characteristic of an associated simplicial complex is a key ingredient in several of the formulas.

Abstract

Several new explicit formulas for certain augmented Hilbert Series measuring maximal and minimal factorization lengths for all numerical semigroups are presented. A weighted type of Euler characteristic of an associated simplicial complex is a key element of some of these formulas.

Papers

The presented work is published in a peer-reviewed paper: Augmented Hilbert series of numerical semigroups (with Christopher O’Neill, Jeske Glenn, and Vadim Ponomarenko) Integers 19 (June 3, 2019), #A32.