Compositions inside a rectangle and unimodality

Authors:
Bruce E. Sagan
Affiliations:
Department of Mathematics, Michigan State University, East Lansing, USA 48824-1027
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2009

Citing 5
Cited 0

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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脳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),驴,c k,l (kl) is unimodal. The problem of giving a combinatorial proof of this fact is discussed, but is still open.