Maximal Newton polygons associated to affine Weyl group elements

One can associate a combinatorial object called the Newton polygon to a group element in GL(n) over certain fields of formal Laurent series. This collection of Newton polygons forms a partially ordered set, and we formulate some of its combinatorial properties. A further refinement is to restrict to the set of Newton polygons which come from group elements in a fixed stratum of the affine Bruhat decomposition. The primary goal of the talk will be to provide a combinatorial algorithm for computing the maximal element in the poset of Newton polygons associated to certain affine Weyl group elements.