Augmented Hilbert series of numerical semigroups


Presented my research from the 2017 San Diego State University Research Experience for Undergraduates during the AMS-MAA-SIAM Special Session on Research in Mathematics by Undergraduates and Students in Post-Baccalaureate Programs at the 2018 Joint Mathematics Meetings in San Diego, California. This talk was funded by an MAA Travel Grant for Undergraduates and by the Mathematics Department at Baylor University.


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.


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.