Tableau sequences, open diagrams, and Baxter families

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 $\varnothing$, 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.

arXiv comment20 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

References in corpus (7)

• Bijections for Baxter Families and Related Objects
• Creative telescoping for rational functions using the Griffiths-Dwork method
• On partitions avoiding 3-crossings
• Enumeration of bilaterally symmetric 3-noncrossing partitions
• A generating tree approach to k-nonnesting partitions and permutations
• A Baxter class of a different kind, and other bijective results using tableau sequences ending with a row shape
• Bijections between oscillating tableaux and (semi)standard tableaux via growth diagrams

Cited by in corpus (5)

• Refined restricted inversion sequences
• Pieri rules for classical groups and equinumeration between generalized oscillating tableaux and semistandard tableaux
• A sequent calculus for the Tamari order
• From Dyck paths to standard Young tableaux
• Bijections for Weyl Chamber walks ending on an axis, using arc diagrams and Schnyder woods