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A decomposition of partitions and numerical sets

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Abstract

The aim of this work is to exhibit a decomposition of partitions of natural numbers and numerical sets. In particular, we obtain a decomposition of a sparse numerical set into the so called hook semigroups which turn out to be primitive. Since each Arf semigroup is sparse, we thus obtain a decomposition of any Arf semigroup into primitive numerical semigroups.

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Authors and Affiliations

  1. Faculty of Commercial Science, Başkent University, Ankara, Turkey

    Halil İbrahim Karakaş

  2. Department of Mathematics, Akdeniz University, 07058, Antalya, Turkey

    Nesrin Tutaş

Authors
  1. Halil İbrahim Karakaş
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  2. Nesrin Tutaş
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Correspondence to Nesrin Tutaş.

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Communicated by Fernando Torres.

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Karakaş, H.İ., Tutaş, N. A decomposition of partitions and numerical sets. Semigroup Forum 101, 704–715 (2020). https://doi.org/10.1007/s00233-019-10080-7

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  • DOI: https://doi.org/10.1007/s00233-019-10080-7

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