On Partitions and Arf Semigroups

Abstract

In this study we examine some combinatorial properties of the Arf semigroup. In previous work, the author and Karakaş, Gümüşbaş defined an Arf partition of a positive integer n. Here, we continue this work and give new results on Arf partitions. In particular, we analyze the relation among an Arf partition, its Young dual diagram, and the corresponding rational Young diagram. Additionally, this study contains some results that present the relations between partitions and Arf semigroup polynomials.

Keywords

• arf numerical semigroup
• young diagram
• partition
• arf partition
• 20m14
• 05a17
• 11d07