A Bijection Between Partially Directed Paths in the SymmetricWedge and Matchings
Identifieur interne : 002794 ( Main/Exploration ); précédent : 002793; suivant : 002795A Bijection Between Partially Directed Paths in the SymmetricWedge and Matchings
Auteurs : Svetlana Poznanovi [États-Unis]Source :
- Annals of Combinatorics [ 0218-0006 ] ; 2011-06-01.
Abstract
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 Janse van Rensburg, Prellberg, and Rechnitzer 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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DOI: 10.1007/s00026-011-0098-1
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