Exponential Dowling structures

Richard Ehrenborg; Margaret A. Readdy

doi:10.1016/j.ejc.2007.11.028

Exponential Dowling structures

Mathematics

Producción científica: Article › revisión exhaustiva

6 Citas (Scopus)

Resumen

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.

Idioma original	English
Páginas (desde-hasta)	311-326
Número de páginas	16
Publicación	European Journal of Combinatorics
Volumen	30
N.º	1
DOI	https://doi.org/10.1016/j.ejc.2007.11.028
Estado	Published - ene 2009

Nota bibliográfica

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.

Financiación

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.

Financiadores	Número del financiador
National Science Foundation Arctic Social Science Program	0200624

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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10.1016/j.ejc.2007.11.028

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title = "Exponential Dowling structures",

abstract = "The notion of exponential Dowling structures is introduced, generalizing Stanley's original theory of exponential structures. Enumerative theory is developed to determine the M{\"o}bius 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 M{\"o}bius 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.",

author = "Richard Ehrenborg and Readdy, \{Margaret A.\}",

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. ",

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AU - Ehrenborg, Richard

AU - Readdy, Margaret A.

N1 - 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.

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N2 - 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.

AB - 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.

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DO - 10.1016/j.ejc.2007.11.028

M3 - Article

AN - SCOPUS:53949108134

SN - 0195-6698

VL - 30

SP - 311

EP - 326

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

IS - 1

ER -

Exponential Dowling structures

Resumen

Nota bibliográfica

Financiación

ASJC Scopus subject areas

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