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Home > Vol 29, No 4 (2009)

Bruce E. Sagan

Michigan State University Department of Mathematics East Lansing MI 48824-1027 USA

Let c ^{k, l} ( n) be the number of compositions (ordered partitions) of the integer n whose Ferrers diagram fits inside a k\times  l rectangle. The purpose of this note is to give a simple, algebraic proof of a conjecture of Vatter that the sequence c ^{k, l} (0), c ^{k, l} (1),\cdots , c ^{k, l} ( kl) is unimodal. The problem of giving a combinatorial proof of this fact is discussed, but is still open.

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