Higher Dimensional Floorplans and Baxter d-Permutations

Explore the mathematical relationship between higher-dimensional floorplans and Baxter d-permutations in this 56-minute research lecture. Learn about 2-dimensional mosaic floorplans as partitions of rectangles by other rectangles with no empty rooms, and discover their known bijection with Baxter permutations. Understand the concept of d-permutations as (d-1)-tuples of permutations and examine the recently introduced Baxter d-permutations that generalize classical Baxter permutations. Discover d-floorplans as generalizations of mosaic floorplans to arbitrary dimensions and examine the construction of their generating tree, noting how the corresponding labels and rewriting rules become significantly more complex in higher dimensions. Investigate a bijection between 2^(d-1)-floorplans and d-permutations characterized by forbidden vincular patterns, and learn why this set of d-permutations is surprisingly contained strictly within the set of Baxter d-permutations. The presentation draws from joint research with Nicolas Bonichon and Adrian Tanasa from Université de Bordeaux, based on arXiv:2504.01116, and provides insights into advanced combinatorial mathematics and permutation theory.