Séminaire Lotharingien de Combinatoire, 82B.23 (2019), 12 pp.
Camille Combe
Cubic realizations of Tamari interval lattices
Abstract.
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.
Received: November 15, 2018.
Accepted: February 17, 2019.
Final version: April 1, 2019.
The following versions are available: