Enumerating maximum length chains in the Tamari lattice

Expositor:  Susanna Fishel

Institución: IMAFI

Lunes 18 de mayo a las 17:00 hrs.
Sala de magíster.

Resumen: Fifty or so years ago Tamari defined a lattice, now known by his name. It has Catalan number of vertices–its Hasse diagram, as an undirected graph, is the one-skeleton of the associahedron– and it is a quotient of the weak Bruhat order. Much is known about this remarkable lattice, but, as Knuth says, the number of maximal chains «remains mysterious.» This is especially odd, because the numbers of maximal chains in many closely related lattices are known. I will describe work with my student Luke Nelson on enumerating maximum length chains. We hope it is progress toward finding the number of maximal chains.