Unimodality and the Reeection Principle
نویسنده
چکیده
We show how lattice paths and the re ection principle can be used to give easy proofs of unimodality results. In particular, we give a \one-line" combinatorial proof of the unimodality of the binomial coe cients. Other examples include products of binomial coe cients, polynomials related to the Legendre polynomials, and a result connected to a conjecture of Simion.
منابع مشابه
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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