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

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 $g$.

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