Vol. 108, No. 1, 1983

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A proof of the Bender-Knuth conjecture

Basil Gordon

Vol. 108 (1983), No. 1, 99–113
Abstract

Let br(nIm) denote the number of r-rowed partitions of n whose parts lie in the set Im = {1,2,,m} and decrease strictly along each row. It is shown that

∑∞              m∏  ∏i
br(n | Im )xn =     (1− xr+i+j−1)∕(1 − xi+j−1).
n=0             i=1 j=1

Mathematical Subject Classification 2000
Primary: 05A17
Secondary: 05A15
Milestones
Received: 30 October 1981
Published: 1 September 1983
Authors
Basil Gordon