A decomposition of partitions and numerical sets


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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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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  • Partition
  • Arf partition
  • Numerical set
  • Young Tableau
  • Hook set
  • Numerical semigroup
  • Arf semigroup
  • Arf closure