#### Alladi Ramakrishnan Hall

#### Tamari Lattice and its Extensions - 1

#### Xavier Viennot

##### University of Bordeaux

*The vertices of the Tamari lattice are binary trees with an order relation defined by a rotation on binary trees. Such lattice can be realized geometrically as a convex polyhedron called the associahedron. Such structure, also called Stasheff polytope, was also introduced in relation with homotopy theory. In recent years, many works have been done on the Tamari lattice. *

I will give a survey of the subject: relation between the 3 structures: hypercube, associahedron and permutohedron (vertices are permutations) at the geometric, algebraic

(Hopf algebras) and combinatorial level; enumeration of the intervals, which are surprisingly the same as the number of triangulations.

Done