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.
Original language | English (US) |
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Pages (from-to) | 46-53 |
Number of pages | 8 |
Journal | Advances in Applied Mathematics |
Volume | 46 |
Issue number | 1-4 |
DOIs | |
State | Published - Jan 2011 |
Keywords
- Bruhat order
- Homotopy type
- Quillen Fiber Lemma
- Weak order
ASJC Scopus subject areas
- Applied Mathematics