Enumerating maximum length chains in the Tamari lattice
Expositor: Susanna Fishel
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.