Vol. 36, No. 2, 1971

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On a partition problem of H. L. Alder

George E. Andrews

Vol. 36 (1971), No. 2, 279–284
Abstract

We study Δd(n) = qd(n) Qd(n), where qd(n) is the number of partitions of n into parts differing by at least d, and Qd(n) is the number of partitions of n into parts congruent to 1 or d + 2( mod d + 3). We prove that Δd(n) +with n for d 4, and that Δd(n) 0 for all n if d = 2s 1,s 4.

Mathematical Subject Classification
Primary: 10.48
Milestones
Received: 1 April 1970
Published: 1 February 1971
Authors
George E. Andrews
Department of Mathematics
The Pennsylvania State University
109 McAllister Building
University Park PA 16802-7000
United States