2019/04/11 by Camille Combe, Combe, Camille
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1904.05841
openalex publication_date 2019/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce cubic coordinates, which are integer words encoding intervals in the Tamari lattices. Cubic coordinates are in bijection with interval-posets, themselves known to be in bijection with Tamari intervals. We show that in each degree the set of cubic coordinates forms a lattice, isomorphic to the lattice of Tamari intervals. Geometric realizations are naturally obtained by placing cubic coordinates in space, highlighting some of their properties. Finally, we consider the cellular structure of these realizations.