... hµis negative. the electronic journal of combinatorics 11(2) (2005), #R18 3Note that the ratio of the coefficients of m1sin the monomial expansions of hλ and hµissλ1, ,λnsµ1, ... +2n)2n22bb,whichislessthan1byourchoiceofb. It follows that the coefficient of m1sin the monomial expansion of hλ− hµis negative and the polynomial x1,π(1)···xn,π(n)− x1,σ(1)···xn,σ(n)isnot MNN. Acknowledgements The ... nonnegativity and the Bruhat orderBrian Drake, Sean Gerrish, Mark SkanderaDept. of Mathematics, Brandeis UniversityMS 050, P.O. Box 9110, Waltham, MA 02454bdrake@math.brandeis.eduDept. of Mathematics,...