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Semigroup Forum

, Volume 88, Issue 3, pp 569–574 | Cite as

On the variety of linear recurrences and numerical semigroups

  • Ivan Martino
  • Luca Martino
RESEARCH ARTICLE

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 a 1<a 2<⋯<a N and M=a N .

Keywords

Numerical semigroups Linear recurrences Generating function 

Notes

Acknowledgements

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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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsStockholm UniversityStockholmSweden
  2. 2.Department of Signal theory and CommunicationsUniversidad Carlos III de MadridMadridSpain

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