A new family of partition identities

David Bressoud

Vol. 77 (1978), No. 1, 71–74

DOI: 10.2140/pjm.1978.77.71

Abstract

The partition function A(n;k) is the number of partitions of n with minimal difference k. Our principal result is that for all k ≧ 1, A(n;k) ≡ B(n;k), where B(n;k) is the number of partitions of n into distinct parts such that for 1 ≦ i ≦ k, the smallest part ≡ i (mod k) is > k ∑ _j=1ⁱ⁻¹r(j), where r(j) is the number of parts ≡ j (mod k). This arises as a corollary to a more general result.

Mathematical Subject Classification 2000

Primary: 10A45, 10A45

Secondary: 05A19

Milestones

Received: 28 December 1976

Published: 1 July 1978