Vol. 77, No. 1, 1978

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A new family of partition identities

David Bressoud

Vol. 77 (1978), No. 1, 71–74
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=1i1r(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
Authors
David Bressoud
Macalester College
Saint Paul MN
United States