论文标题
为花圈产品的单一字符生成功能
Generating functions for monomial characters of wreath products $\mathbb Z/d \mathbb Z \wr \mathfrak S_n$
论文作者
论文摘要
令$ \ MATHBB Z/D \ MATHBB Z \ WR \ MATHFRAK S_N $用对称组$ \ Mathfrak S_N $表示环状组$ \ Mathbb z/d \ Mathbb z $的花环产品。我们为$ \ Mathbb z/d \ Mathbb Z \ wr \ Mathfrak s_n $的单一字符（诱导的一维）字符定义生成功能，并根据决定因素和永久性来表达这些功能。这扩展了Littlewood的工作（{\ em的群体特征和组的形式}，1940年），以及Merris和Watkins（{\ em lineal algebra appl。}，{\ bf 64}，1985年，1985年）在生成函数的$ \ \ \ \ m mathfrak s_n $的单一字符上生成功能。
Let $\mathbb Z/d\mathbb Z \wr \mathfrak S_n$ denote the wreath product of the cyclic group $\mathbb Z/d\mathbb Z$ with the symmetric group $\mathfrak S_n$. We define generating functions for monomial (induced one-dimensional) characters of $\mathbb Z/d\mathbb Z \wr \mathfrak S_n$ and express these in terms of determinants and permanents. This extends work of Littlewood ({\em The Theory of Group Characters and Representations of Groups}, 1940) and Merris and Watkins ({\em Linear Algebra Appl.}, {\bf 64}, 1985) on generating functions for the monomial characters of $\mathfrak S_n$.
