On the variety of linear recurrences and numerical semigroups

Abstract

In this work, we prove the existence of linear recurrences of order M with a non-trivial solution vanishing exactly on the set of gaps (or a subset) of a numerical semigroup S finitely generated by a1 < a2 <...< aN and M = aN. Keywords: numerical semigroups, linear recurrences, generating function.

arXiv commentAccepted on Semigroup Forum