The Electronic Journal of Combinatorics
We show that five nonnegativity properties of polynomials coincide when restricted to polynomials of the form x1, pi(1) ... xn,pi(n) - x1, sigma(1) ... xn, sigma(n), where $\pi and sigma are permutations in Sn. In particular, we show that each of these properties may be used to characterize the Bruhat order on Sn.
Drake, Brian; Gerrish, Sean; and Skandera, Mark, "Monomial Nonnegativity and the Bruhat Order" (2005). Open Dartmouth: Faculty Open Access Articles. 2326.