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arXiv · 0803.4233

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

Svetlana Poznanovik
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Abstract

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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Svetlana Poznanovik. 2008-03-29. A Bijection Between Partially Directed Paths in the Symmetric Wedge and Matchings. https://arxiv.org/abs/0803.4233

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