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

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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, . . .}.

Original languageEnglish
Pages (from-to)709-725
Number of pages17
JournalEuropean Journal of Combinatorics
Volume17
Issue number8
DOIs
StatePublished - Nov 1996

Bibliographical note

Funding Information:
We thank Gábor Hetyei, Jacques Labelle and Richard Stanley for reading preliminary versions of this paper. We would also like to thank the referees for their suggestions. The first author was supported by the Centre de Recherches Mathématiques at the Universitéde Montréal and LACIM at the Universitédu Québec à Montréal. The second author was supported by LACIM at the Université du Québec à Montréal.

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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