Résumé : A 2-dimensional mosaic floorplan is a partition of a rectangle by other rectangles with no empty rooms. These partitions (considered up to some deformations) are known to be in bijection with Baxter permutations. A d-permutation is a (d-1)-tuple of permutations. In this talk, I will present a work in collaboration with Nicolas Bonichon and Adrian Tanasa where we introduce the d-floorplans which generalise the mosaic floorplans to arbitrary dimensions. I will first present the construction of their generating tree for which the corresponding labels and rewriting rules appear to be significantly more involved in higher dimensions. Then, I will present a bijection between the 2^{d-1}-floorplans and d-permutations characterised by forbidden vincular patterns, generalizing the bijection with Baxter permutations in the case d=2. Finally, I will present some work in progress on the "segments" of the 2^{d-1}-floorplans which relate d-floorplans to another class of d-permutations.

Dernière modification : Wednesday 29 October 2025

Contact pour cette page : Cyril.Banderier at lipn.univ-paris13.fr