Geodesic
Compositions inside a rectangle and unimodality
Journal of Algebraic Combinatorics, Tome 29 (2009) no. 4, pp. 405-411.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Keywords: keywords composition, integer partition, unimodal 
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     author = {Sagan, Bruce E.},
     title = {Compositions inside a rectangle and unimodality},
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Sagan, Bruce E. Compositions inside a rectangle and unimodality. Journal of Algebraic Combinatorics, Tome 29 (2009) no. 4, pp. 405-411. http://geodesic.mathdoc.fr/item/JAC_2009__29_4_a7/