Compositions inside a rectangle and unimodality

Details Compositions inside a rectangle and unimodality Compositions inside a rectangle and unimodality

2007-07-06

arxiv.org/abs/0707.1052v1

Mathematics

Combinatorics

9 pages, 1 figure, see related papers at http://www.math.msu.edu/~sagan

Scientific paper

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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