### Le 15-11-2019 : Camille Combe (IRMA)

**Cubic realizations of Tamari interval lattices***We introduce cubic coordinates, which are integer words encoding intervals in the Tamari lattices.<br /><br />
Cubic coordinates are in bijection with interval-posets, themselves known to be in bijection with Tamari intervals.<br /><br />
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We will see that in each degree the set of cubic coordinates forms a lattice, isomorphic to the lattice of Tamari intervals. <br /><br />
Geometric realizations are naturally obtained by placing cubic coordinates in space, highlighting some of their properties. <br /><br />
We will present the cellular structure of these realizations. Finally, we will see a proof generalizing the result of Björner and Wachs about the EL-shellability of Tamari posets for Tamari interval posets.<br /><br />
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