On the variety of linear recurrences and numerical semigroups
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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 a 1<a 2<⋯<a N and M=a N .
KeywordsNumerical semigroups Linear recurrences Generating function
We would like to thank Ralf Fröberg (Stockholm University, Department of Mathematics) and Boris Shapiro (Stockholm University, Department of Mathematics) for their help and several suggestions. Furthermore, we thank the reviewers for their useful comments which have helped us to improve this manuscript. Moreover, this work has been partially supported by Government of Spain (project COMONSENS, id. CSD2008-00010, project DEIPRO, and project COMPREHENSION, id. TEC2012-38883-C02-01).
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