TWISTED INCIDENCE ALGEBRAS AND KAZHDAN-LUSZTIG-STANLEY FUNCTIONS

FRANCESCO BRENTI

Abstract. We introduce a new multiplication in the incidence algebra of a partially ordered set, and study the resulting algebra. As an application of the properties of this algebra we obtain a combinatorial formula for the Kazhdan-Lusztig-Stanley function of a poset. As special cases we obtain new combinatorial formulas for the parabolic and inverse parabolic Kazhdan-Lusztig polynomials, for the generalized (toric) h-vector of an Eulerian poset, and for the Lusztig-Vogan polynomials.