Bijections for Weyl Chamber walks ending on an axis, using arc diagrams and Schnyder woods release_42q5jocf7rahfjgoc45llcg654

by Julien Courtiel, Éric Fusy, Mathias Lepoutre, Marni Mishna

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2017  

Abstract

In the study of lattice walks there are several examples of enumerative equivalences which amount to a trade-off 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 modification 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.
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Date   2017-03-15
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arXiv  1611.04489v2
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