Nestings of Matchings and Permutations and North Steps in PDSAWs
Combinatorics
2008-04-11 v4
Abstract
We present a simple bijective proof of the fact that matchings of [2n] with N nestings are equinumerous to partially directed self avoiding walks confined to the symmetric wedge defined by y=+-x, with n east steps and N north steps. A very similar construction connects permutations with N nestings and PDSAWs remaining below the x-axis, again with N north steps. Furthermore, both bijections transport several combinatorially meaningful parameters.
Keywords
Cite
@article{arxiv.0712.2804,
title = {Nestings of Matchings and Permutations and North Steps in PDSAWs},
author = {Martin Rubey},
journal= {arXiv preprint arXiv:0712.2804},
year = {2008}
}
Comments
11 pages, 7 figures, corrected some inaccuracies and minor mistakes