Réalisation cubique du poset des intervalles de Tamari

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. We consider the cellular structure of these realizations. Finally, we show that the poset of cubic coordinates is shellable.
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https://hal.archives-ouvertes.fr/hal-02088449
Contributor : Camille Combe <>
Submitted on : Tuesday, April 2, 2019 - 8:23:25 PM
Last modification on : Tuesday, April 16, 2019 - 8:47:25 AM

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Camille Combe. Réalisation cubique du poset des intervalles de Tamari. 2019. ⟨hal-02088449⟩

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