Tableau sequences, open diagrams, and Baxter families

Sophie Burrill, Julien Courtiel, Eric Fusy, Stephen Melczer, Marni Mishna
2016 European journal of combinatorics (Print)  
Walks on Young's lattice of integer partitions encode many objects of algebraic and combinatorial interest. Chen et al. established connections between such walks and arc diagrams. We show that walks that start at ∅, end at a row shape, and only visit partitions of bounded height are in bijection with a new type of arc diagram -- open diagrams. Remarkably two subclasses of open diagrams are equinumerous with well known objects: standard Young tableaux of bounded height, and Baxter permutations.
more » ... We give an explicit combinatorial bijection in the former case.
doi:10.1016/j.ejc.2016.05.011 fatcat:7ewn6ibhizef7ctmnjldciqbeu