Baxter Tree-like Tableaux
Jean-Christophe Aval, Adrien Boussicault, Mathilde Bouvel, Olivier, Guibert, Matteo Silimbani

TL;DR
This paper introduces a new subclass of tree-like tableaux linked to Baxter numbers, establishes bijections with other Baxter-enumerated objects, and provides new enumerative results and a novel class of floorplans.
Contribution
It defines and studies Baxter tree-like tableaux, unifies bijections among Baxter objects, and introduces alternating floorplans with their enumeration.
Findings
Baxter tree-like tableaux are enumerated by Baxter numbers.
Established bijections with floorplans, twisted Baxter permutations, and lattice path triples.
Enumerated a new class called alternating floorplans.
Abstract
Tree-like tableaux are objects in bijection with alternative or permutation tableaux. They have been the subject of a fruitful combinatorial study for the past few years. In the present work, we define and study a new subclass of tree-like tableaux enumerated by Baxter numbers. We exhibit simple bijective links between these objects and three other combinatorial classes: (packed or mosaic) floorplans, twisted Baxter permutations and triples of non-intersecting lattice paths. From several (and unrelated) works, these last objects are already known to be enumerated by Baxter numbers, and our main contribution is to provide a unifying approach to bijections between Baxter objects, where Baxter tree-like tableaux play the key role. We moreover get new enumerative results about alternating twisted Baxter permutations. Finally, we define a new subfamily of floorplans, which we call…
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Advanced Topics in Algebra
