NoteOn the non-negativity of the complete cd-index

The complete cd-index of a Bruhat interval is a non-commutative polynomial in the variables c  and d, which was introduced by Billera and Brenti and conjectured to have non-negative coefficients. For a cd-monomial M containing at most one d, i.e.,  M=ci or M=cidcj(i,j≥0), Karu showed that the coefficient of M is non-negative. In this paper, we show that when M=dcidcj(i,j≥0), the coefficient of M is non-negative.