On a partition problem of H. L. Alder

George E. Andrews

Vol. 36 (1971), No. 2, 279–284

DOI: 10.2140/pjm.1971.36.279

Abstract

We study Δ_d(n) = q_d(n) −Q_d(n), where q_d(n) is the number of partitions of n into parts differing by at least d, and Q_d(n) is the number of partitions of n into parts congruent to 1 or d + 2( mod d + 3). We prove that Δ_d(n) → +∞ with n for d ≧ 4, and that Δ_d(n) ≧ 0 for all n if d = 2^s − 1,s ≧ 4.

Mathematical Subject Classification

Primary: 10.48

Milestones

Received: 1 April 1970

Published: 1 February 1971