Nestings of Matchings and Permutations and North Steps in PDSAWs

Details Nestings of Matchings and Permutations and North Steps in PDSAWs Nestings of Matchings and Permutations and North Steps in PDSAWs

2007-12-17

arxiv.org/abs/0712.2804v4

Mathematics

Combinatorics

11 pages, 7 figures, corrected some inaccuracies and minor mistakes

Scientific paper

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.

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