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A Bijection Between Partially Directed Paths in the SymmetricWedge and Matchings
Svetlana Poznanović
Department of Mathematics, Texas A&M University, College Station, TX 77843, USA
spoznan@math.tamu.edu
Annals of Combinatorics 15 (2) pp.331-339 April, 2011
AMS Subject Classification: 05A16; 60C05, 60F05
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.
Keywords: partially directed path, matching, nesting

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