A decomposition of partitions and numerical sets

KARAKAŞ H. İ., TUTAŞ N.

SEMIGROUP FORUM, vol.101, no.3, pp.704-715, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 101 Issue: 3
  • Publication Date: 2020
  • Doi Number: 10.1007/s00233-019-10080-7
  • Journal Name: SEMIGROUP FORUM
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.704-715
  • Keywords: Partition, Arf partition, Numerical set, Young Tableau, Hook set, Numerical semigroup, Arf semigroup, Arf closure
  • Akdeniz University Affiliated: Yes

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.