A Bijection Between Partially Directed Paths in the Symmetric Wedge and Matchings

Details A Bijection Between Partially Directed Paths in the Symmetric Wedge and Matchings A Bijection Between Partially Directed Paths in the Symmetric Wedge and Matchings

2008-03-29

arxiv.org/abs/0803.4233v1

Mathematics

Combinatorics

10 pages, 5 figures

Scientific paper

We give a bijection between partially directed paths in the symmetric wedge y= +/-x and matchings, which sends north steps to nestings. This gives a bijective proof of a result of Prellberg et al. that was first discovered through the corresponding generating functions: the number of partially directed paths starting at the origin confined to the symmetric wedge y= +/-x with k north steps is equal to the number of matchings on [2n] with k nestings.

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