## Higher Bruhat Orders and Higher Stasheff-Tamari Posets

**Hugh Thomas **

(UWO)

Abstract: The higher Bruhat orders B(n,d) were introduced by Manin and

Schechtman as generalizations of weak Bruhat order: B(n,1) is weak
Bruhat

order on the symmetric group S_n, and B(n,0) is the Boolean lattice Q_n.

The higher Stasheff-Tamari posets are defined as partial orders on the set

of triangulations of a cyclic polytope. There are reformulations of
these

families of posets which make the connections between them more obvious:
a

convex-geometric reformulation of the higher Bruhat orders due to Kapranov

and Voevodsky, and a combinatorial reformulation of the Stasheff-Tamari

posets due to myself. I will discuss various maps between higher

Stasheff-Tamari posets and higher Bruhat orders which specialize to

familar maps between S_n and Q_{n-1}, and from S_n to planar binary trees.