The proof of a conjecture of Simion for certain partitions

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The proof of a conjecture of Simion for certain partitions

Simion has a conjecture concerning the number of lattice paths in a rectangular grid with the Ferrer's diagram of a partition removed. The conjecture concerns the unimodality of this number over a sequence of rectangles with the sum of the length and width being constant and with a constant partition. This paper demonstrates this unimodality if the partition is symmetric or if the Ferrer's diag...

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A Simple Proof of a Conjecture of Simion

Simion had a unimodality conjecture concerning the number of lattice paths in a rectangular grid with the Ferrers diagram of a partition removed. Hildebrand recently showed the stronger result that these numbers are log concave. Here we present a simple proof of Hildebrand’s result.

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ژورنال

عنوان ژورنال: Discrete Mathematics

سال: 2000

ISSN: 0012-365X

DOI: 10.1016/s0012-365x(00)00111-4