On the Number of Partitions of n into Exactly m Parts Whose Even Parts are Distinct

  • Dhanasin Namphaisaal
  • Teerapat Srichan

Abstract

Let ped(n) be the number of partitions of n whose even parts are distinct and whose odd parts are unrestricted. For a positive integer m, let ped(n,m) be the number of all possible partitions of the number n into exactly m parts whose even parts are distinct and whose odd parts are unrestricted.

In this paper, we give new recurrence formulas for ped(n,m) as well as explicit formulas for ped(n,m), when m=2,3 and m=4. For a positive integer q and j{0,1,2,,q1}, we also give a recurrence formula for pq,j(n,m) the number of partitions of n into m parts such that the parts congruent to j modulo q are distinct, where other parts are unrestricted.

Published
2024-08-23
Article Number
P3.19