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- W1997859393 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." @default.
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- W1997859393 date "2009-01-01" @default.
- W1997859393 modified "2023-10-18" @default.
- W1997859393 title "Exponential Dowling structures" @default.
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- W1997859393 doi "https://doi.org/10.1016/j.ejc.2007.11.028" @default.
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