Glenn Hurlbert, Vikram Kamat
Published 2006-09-07Version 1
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 \binom{2n}{n} 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.
A uniformly distributed parameter on a class of lattice paths
Even and Odd Pairs of Lattice Paths with Multiple Intersections
Counting pairs of lattice paths by intersections
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