Bijections for Weyl Chamber Walks Ending on an Axis, Using Arc Diagrams and Schnyder Woods

In the study of lattice walks there are several examples of enumerative equivalences which amount to a trade-o between domain and endpoint constraints. We present a family of such bijections for simple walks in Weyl chambers which use arc diagrams in a natural way. One consequence is a set of new bijections for standard Young tableaux of bounded height. A modi cation of the argument in two dimensions yields a bijection between Baxter permutations and walks ending on an axis, answering a recent question of Burrill et al. (2016). Some of our arguments (and related results) are proved using Schnyder woods. Our strategy for simple walks extends to any dimension and yields a new bijective connection between standard Young tableaux of height at most 2k and certain walks with prescribed endpoints in the k-dimensional Weyl chamber of type D.