Two New Bijections on Lattice Paths
Combinatorics
2007-05-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.math/0609222,
title = {Two New Bijections on Lattice Paths},
author = {Glenn Hurlbert and Vikram Kamat},
journal= {arXiv preprint arXiv:math/0609222},
year = {2007}
}