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Unimodality and the reflection principle

Bruce Sagan
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Abstract

We show how lattice paths and the reflection 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 coefficients. Other examples include products of binomial coefficients, polynomials related to the Legendre polynomials, and a result connected to a conjecture of Simion.

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Bruce Sagan. 1997-12-03. Unimodality and the reflection principle. https://arxiv.org/abs/math/9712215

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