Nestings of Matchings and Permutations and North Steps in PDSAWs

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

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Combinatorics, 05A15

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http://salesiana.dossiersoluciones.com/handle/123456789/158462

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0712.2804
 http://arxiv.org/abs/0712.2804

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arXiv