Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6419687 | Advances in Applied Mathematics | 2011 | 8 Pages |
Abstract
In this note we construct a poset map from a Boolean algebra to the Bruhat order which unveils an interesting connection between subword complexes, sorting orders, and certain totally nonnegative spaces. This relationship gives a simple new proof that the proper part of Bruhat order is homotopy equivalent to the proper part of a Boolean algebra - that is, to a sphere. We also obtain a geometric interpretation for sorting orders. We conclude with two new results: that the intersection of all sorting orders is the weak order, and the union of sorting orders is the Bruhat order.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Drew Armstrong, Patricia Hersh,