Abstract
We construct 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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Acknowledgements
The author was partially supported FAPDF-Brazil (grant 23072.91.49580.29052018). Part of this paper was presented in the “INdAM: International meeting on numerical semigroups” (2018) at Cortona, Italy. I am grateful to the referee for their comments, suggestions and corrections that allowed to improve this version of the paper.
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Bernardini, M. (2020). Counting Numerical Semigroups by Genus and Even Gaps via Kunz-Coordinate Vectors. In: Barucci, V., Chapman, S., D'Anna, M., Fröberg, R. (eds) Numerical Semigroups . Springer INdAM Series, vol 40. Springer, Cham. https://doi.org/10.1007/978-3-030-40822-0_1
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DOI: https://doi.org/10.1007/978-3-030-40822-0_1
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