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arXiv · 0707.1052

Compositions inside a rectangle and unimodality

Bruce E. Sagan
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Abstract

Let c^{k,l}(n) be the number of compositions (ordered partitions) of the integer n whose Ferrers diagram fits inside a k-by-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), ..., 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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Bruce E. Sagan. 2007-07-06. Compositions inside a rectangle and unimodality. https://arxiv.org/abs/0707.1052

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