The colection of partitions of positive integers, the collection of Young diagrams and the collection of numerical sets are in one to one correspondance with each other. Therefore any concept in one of these collections has its counterpart in the other collections. For example the concept of Arf numerical semigroup in the collection of numerical sets, gives rise to the concept of Arf partition of a positive integer in the collection of partitions. Several characterizations of Arf partitions have been given in recent works. In this talk we wil characterize Arf partitions of maximal length of positive integers.
This is a joint work with Nesrin Tutaş and Nihal Gümüşbaş from Akdeniz University.