# Compositions inside a rectangle and unimodality - Mathematics > Combinatorics

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Abstract: Let c^{k,l}n be the number of compositions ordered partitions of theinteger n whose Ferrers diagram fits inside a k-by-l rectangle. The purpose ofthis note is to give a simple, algebraic proof of a conjecture of Vatter thatthe sequence c^{k,l}0, c^{k,l}1,

., c^{k,l}kl is unimodal. The problemof giving a combinatorial proof of this fact is discussed, but is still open.

Author: ** Bruce E. Sagan Michigan State U.**

Source: https://arxiv.org/