Counting numerical semigroups by genus and even gaps via Kunz-coordinate vectors

Matheus Bernardini

doi:10.1007/978-3-030-40822-0_1

paper

Counting numerical semigroups by genus and even gaps via Kunz-coordinate vectors

arXiv:1906.07310 · doi:10.1007/978-3-030-40822-0_1

Abstract

We contruct a one-to-one correspondence between a subset of numerical semigroups with genus $g$ and $γ$ even gaps and the integer points of a rational polytope. In particular, we give an overview to apply this correspondence to try to decide if the sequence $(n_{g})$ is increasing, where $n_{g}$ denotes the number of numerical semigroups with genus $g$ .

8 pages