The r-cubical lattice and a generalization of the cd-index

Abstract

In this paper we generalize the cd-index of the cubical lattice to an r-cd-index, which we denote by ψ(r). The coefficients of ψ(r) enumerate augmented André r-signed permutations, a generalization of Purtill's work relating the cd-index of the cubical lattice and signed André permutations. As an application we use the r-cd-index to determine that the extremal configuration which maximizes the Möbius function of arbitrary rank selections, where all the ri's are greater than one, is the odd alternating ranks, {1, 3, 5, . . .}. © 1996 Academic Press Limited.