Exponential Dowling structures
Exponential Dowling structures
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指数道林结构
DOI：
10.1016/j.ejc.2007.11.028
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Margaret A. Readdy
中科院分区：
文献类型：
--
作者：
R. Ehrenborg;Margaret A. Readdy
引入了指数道林结构的概念，推广了Stanley的指数结构理论。枚举理论的发展，以确定指数道林结构的莫比乌斯函数，包括这些结构的类型满足半群条件的元素的限制。斯坦利对与指数结构相关的排列的研究导致了对指数道林结构的类似研究。特别地，对于扩展的r-可分划分格，我们证明了Möbius函数在符号之前是rn+k个元素上的对称群中具有下降集{r，2 r，.，nr}的置换数.利用Wachs对r-可分分格的EL-标号，证明了扩展的r-可分格是EL-可壳的.
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 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.