2006/09/07 by Glenn Hurlbert, Hurlbert, Glenn, Vikram Kamat +1
Mathematics · #05A15 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A15
paper · pdf · doi:10.48550/arxiv.math/0609222
arxiv created 2006/09/07 · arxiv updated 2009/12/01
Suppose 2n voters vote sequentially for one of two candidates. For how many such sequences does one candidate have strictly more votes than the other at each stage of the voting? The answer is \binom2nn and, while easy enough to prove using generating functions, for example, only two combinatorial proofs exist, due to Kleitman and Gessel. In this paper we present two new (far simpler) bijective proofs.