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On the variety of linear recurrences and numerical semigroups

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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 .

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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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Authors and Affiliations

  1. Department of Mathematics, Stockholm University, Stockholm, Sweden

    Ivan Martino

  2. Department of Signal theory and Communications, Universidad Carlos III de Madrid, Leganes, Madrid, Spain

    Luca Martino

Authors
  1. Ivan Martino
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  2. Luca Martino
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Correspondence to Ivan Martino.

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Communicated by Fernando Torres.

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Martino, I., Martino, L. On the variety of linear recurrences and numerical semigroups. Semigroup Forum 88, 569–574 (2014). https://doi.org/10.1007/s00233-013-9551-2

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  • DOI: https://doi.org/10.1007/s00233-013-9551-2

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