Arithmetic functions | Integer partitions

Rank of a partition

In mathematics, particularly in the fields of number theory and combinatorics, the rank of a partition of a positive integer is a certain integer associated with the partition. In fact at least two different definitions of rank appear in the literature. The first definition, with which most of this article is concerned, is that the rank of a partition is the number obtained by subtracting the number of parts in the partition from the largest part in the partition. The concept was introduced by Freeman Dyson in a paper published in the journal Eureka. It was presented in the context of a study of certain congruence properties of the partition function discovered by the Indian mathematical genius Srinivasa Ramanujan. A different concept, sharing the same name, is used in combinatorics, where the rank is taken to be the size of the Durfee square of the partition. (Wikipedia).

Rank of a partition
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Related pages

Srinivasa Ramanujan | Durfee square | Ramanujan's congruences | Congruence relation | Mathematics | Partition (number theory) | Integer | Combinatorics | Partition function (number theory) | Crank of a partition | Number theory