第一类和第二类Dowling格的退化Whitney数的研究
A Study on degenerate Whitney numbers of the first and second kinds of Dowling lattices
摘要：
Dowling对任意n元有限集和任意m阶有限乘法群G构造了Dowling格Qn（G），它是一个有限的几何格.他还定义了惠特尼数的第一和第二种任何有限的几何格。道林格Qn（G）的这些数是第一类Whitney数Vm（n，k）和第二类Whitney数Wm（n，k），它们由类Stirling数关系给出。在本文中，通过“退化”这样的关系，我们引入了退化的第一类和第二类Whitney数，并调查，除其他事项外，生成函数，递归关系和各种显式表达式。作为这两类退化Whitney数的进一步推广，我们还考虑了这两类退化r-Whitney数。
英文摘要：
Dowling constructed Dowling lattice Qn(G), for any finite set with n elements and any finite multiplicative group G of order m, which is a finite geometric lattice. He also defined the Whitney numbers of the first and second kinds for any finite geometric lattice. These numbers for the Dowling lattice Qn(G) are the Whitney numbers of the first kind Vm(n,k) and those of the second kind Wm(n,k), which are given by Stirling number-like relations. In this paper, by `degenerating' such relations we introduce the degenerate Whitney numbers of the first kind and those of the second kind and investigate, among other things, generating functions, recurrence relations and various explicit expressions for them. As further generalizations of the degenerate Whitney numbers of both kinds, we also consider the degenerate r-Whitney numbers of both kinds.
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