A decomposition of partitions and numerical sets

KARAKAŞ H. İ., TUTAŞ N.

SEMIGROUP FORUM, cilt.101, sa.3, ss.704-715, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 101 Sayı: 3
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1007/s00233-019-10080-7
  • Dergi Adı: SEMIGROUP FORUM
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.704-715
  • Anahtar Kelimeler: Partition, Arf partition, Numerical set, Young Tableau, Hook set, Numerical semigroup, Arf semigroup, Arf closure
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.