Exponential Dowling structures

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

The notion of exponential Dowling structures is introduced, generalizing Stanley's original theory of exponential structures. Enumerative theory is developed to determine the Möbius function of exponential Dowling structures, including a restriction of these structures to elements whose types satisfy a semigroup condition. Stanley's study of permutations associated with exponential structures leads to a similar vein of study for exponential Dowling structures. In particular, for the extended r-divisible partition lattice we show that the Möbius function is, up to a sign, the number of permutations in the symmetric group on r n + k elements having descent set {r, 2 r, ..., n r}. Using Wachs' original EL-labeling of the r-divisible partition lattice, the extended r-divisible partition lattice is shown to be EL-shellable.

Original languageEnglish
Pages (from-to)311-326
Number of pages16
JournalEuropean Journal of Combinatorics
Volume30
Issue number1
DOIs
StatePublished - Jan 2009

Bibliographical note

Funding Information:
The first author was partially supported by National Science Foundation grant 0200624. Both authors thank the Mittag-Leffler Institute where a portion of this research was completed during the Spring 2005 program in Algebraic Combinatorics. The authors also thank the referee for suggesting additional references.

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Fingerprint

Dive into the research topics of 'Exponential Dowling structures'. Together they form a unique fingerprint.

Cite this