Sorting orders, subword complexes, Bruhat order and total positivity

Drew Armstrong, Patricia Hersh

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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 languageEnglish (US)
Pages (from-to)46-53
Number of pages8
JournalAdvances in Applied Mathematics
Issue number1-4
StatePublished - Jan 2011


  • Bruhat order
  • Homotopy type
  • Quillen Fiber Lemma
  • Weak order

ASJC Scopus subject areas

  • Applied Mathematics


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