The Electronic Journal of Combinatorics
We give two new criteria by which pairs of permutations may be compared in defining the Bruhat order (of type $A$). One criterion utilizes totally nonnegative polynomials and the other utilizes Schur functions.
Drake, Brian; Gerrish, Sean; and Skandera, Mark, "Two New Criteria for Comparison in the Bruhat Order" (2004). Open Dartmouth: Faculty Open Access Articles. 2327.