A Bijection Between Partially Directed Paths in the Symmetric Wedge and Matchings
Combinatorics
2008-04-01 v1
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.
Keywords
Cite
@article{arxiv.0803.4233,
title = {A Bijection Between Partially Directed Paths in the Symmetric Wedge and Matchings},
author = {Svetlana Poznanovik},
journal= {arXiv preprint arXiv:0803.4233},
year = {2008}
}
Comments
10 pages, 5 figures