A Bijection Between Partially Directed Paths in the SymmetricWedge and Matchings

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.