Weak Order Cubical Complexes

Segrei Ovchinnikov

San Francisco State University

Abstract

In this talk we will present geometric models of the set WO of weak orders
on a finite set X. In particular, WO is modeled as a set of vertices of a cubical
subcomplex of a cube. This approach is an alternative to the usual representation
of WO by means of a weak order polytope. We will also describe an application
of this model in the framework of media theory.