Karakas, Halil IbrahimTutas, Nesrin2021-08-192021-08-1920200037-1912http://hdl.handle.net/11727/6288The 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.enginfo:eu-repo/semantics/closedAccessPartitionArf partitionNumerical setYoung TableauHook setNumerical semigroupArf semigroupArf closureArticle10137047150005053297000012-s2.0-85077280212