Monomial nonnegativity and the Bruhat order

Abstract

We show that five nonnegativity properties of polynomials coincide when restricted to polynomials of the form x1; π (1) xn; π (n) - x1;σ(1) xn;σ(n), where π and σ are permutations in Sn. In particular, we show that each of these properties may be used to characterize the Bruhat order on Sn.