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arXiv · 1009.4202

Exponential Dowling structures

Richard Ehrenborg·Margaret Readdy
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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 the Möbius function is, up to a sign, the number of permutations in the symmetric group on rn+k elements having descent set {r, 2r, ..., nr}. 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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Richard Ehrenborg, Margaret Readdy. 2010-09-21. Exponential Dowling structures. https://arxiv.org/abs/1009.4202

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