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Journal Articles The Australasian Journal of Combinatorics Year : 2023

Baxter Tree-like Tableaux

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 alternating floorplans, and we enumerate these combinatorial objects.

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hal-03385234 , version 1 (19-10-2021)

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Jean-Christophe Aval, Adrien Boussicault, Mathilde Bouvel, Olivier Guibert, Matteo Silimbani. Baxter Tree-like Tableaux. The Australasian Journal of Combinatorics, 2023, 86 (1), pp.24--75. ⟨10.48550/arXiv.2108.06212⟩. ⟨hal-03385234⟩
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