Signed Mahonian on parabolic quotients of colored permutation groups

Sen Peng Eu, Tung Shan Fu, Yuan Hsun Lo*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number102269
JournalAdvances in Applied Mathematics
Publication statusPublished - 2022 Jan


  • Colored permutations
  • Insertion lemma
  • Parabolic quotients
  • Signed Mahonian

ASJC Scopus subject areas

  • Applied Mathematics


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