论文标题
签名的欧拉 - 马洪尼人身份
Signed Euler-Mahonian identities
论文作者
论文摘要
Désarménien和Foata在1992年在$ \ Mathfrak {s} _n $上签名的Eulerian多项式与经典的Eulerian多项式之间的关系，并在1992年给出了一个精致的版本，称为Euler-Mahonian身份，同时又提出了签名的Euler-Mahonian身份，同时又提出了同一年度。通过概括此本文，在本文中，我们将上述结果扩展到$ b_n $，$ d_n $的类型的Coxeter组和复杂的反射组$ g（r，1，n）$，其中“符号”被视为任何一维字符。一些获得的身份可以进一步限制在某些特定的排列集中。我们还为$ b_n $和$ d_n $的类型提供了一些新的有趣的标志性多项式。
A relationship between signed Eulerian polynomials and the classical Eulerian polynomials on $\mathfrak{S}_n$ was given by Désarménien and Foata in 1992, and a refined version, called signed Euler-Mahonian identity, together with a bijective proof were proposed by Wachs in the same year. By generalizing this bijection, in this paper we extend the above results to the Coxeter groups of types $B_n$, $D_n$, and the complex reflection group $G(r,1,n)$, where the `sign' is taken to be any one-dimensional character. Some obtained identities can be further restricted on some particular set of permutations. We also derive some new interesting sign-balance polynomials for types $B_n$ and $D_n$.
