Tableau sequences, open diagrams, and Baxter families
Combinatorics
2018-05-28 v1
Abstract
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. We give an explicit combinatorial bijection in the former case.
Cite
@article{arxiv.1506.03544,
title = {Tableau sequences, open diagrams, and Baxter families},
author = {Sophie Burrill and Julien Courtiel and Eric Fusy and Stephen Melczer and Marni Mishna},
journal= {arXiv preprint arXiv:1506.03544},
year = {2018}
}
Comments
20 pages; Text overlap with arXiv:1411.6606. This is the full version of that extended abstract. Conjectures from that work are proved in this work