1997/12/03 by Bruce Sagan
Mathematics · #math.CO
published as Ars Combin. 48 (1998), 65-72 · 7 pages (plus cover and abstract)
arxiv created 1997/12/03 · arxiv updated 2009/11/30
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.