论文标题
在彩色置换组的抛物线商上签名的Mahonian
Signed Mahonian on Parabolic Quotients of Colored Permutation Groups
论文作者
论文摘要
我们研究了具有彩色置换组的每个一维特征，称为签名的Mahonian多项式，这是标志主要指数的生成多项式，这是彩色置换组，这是与对称组的环状群的花环产物。使用HAN和HAGLUND-LOEHR-REMEL的插入引le以及Eu等人建立的签名扩展，我们将签名的Mahonian多项式在有色置换组的抛物线亚组的商上，用于各种coset Systems of COSET Systems of COSET代表在子序列限制方面的各种系统。这概括了由于Caselli以及Eu等人而导致的对称组的抛物线商的相关工作。作为副产品，我们得出了一个产品公式，该产品公式概括了Biagioli对签名的Mahonian在均匀签名的置换组上的结果。
We study the generating polynomial of the flag major index with each one-dimensional character, called signed Mahonian polynomial, over the colored permutation group, the wreath product of a cyclic group with the symmetric group. Using the insertion lemma of Han and Haglund-Loehr-Remmel and a signed extension established by Eu et al., we derive the signed Mahonian polynomial over the quotients of parabolic subgroups of the colored permutation group, for a variety of systems of coset representatives in terms of subsequence restrictions. This generalizes the related work over parabolic quotients of the symmetric group due to Caselli as well as to Eu et al. As a byproduct, we derive a product formula that generalizes Biagioli's result about the signed Mahonian on the even signed permutation groups.
