Generalized Tamari order

Abstract

In [2], M. Carr and S. Devadoss introduced the notion of tubing on a finite simple graph G. When G is the linear graph Ln, with n vertices, the polytope K Ln is the Stasheff polytope or associahedron. Our goal is to describe a partial order on the set of tubings of a simple graph, which generalizes the Tamari order on the set of vertices of the associahedron. For certain families of graphs, this order induces an associative product on the vector space spanned by the tubings of all the graphs.