An inversion statistic on the generalized symmetric groups

Arslan H., Altoum A., Zaarour M.

ADVANCES IN APPLIED MATHEMATICS, cilt.154, ss.1-20, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 154
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1016/j.aam.2023.102655
  • Dergi Adı: ADVANCES IN APPLIED MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Compendex, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.1-20
  • Erciyes Üniversitesi Adresli: Evet

Özet

In this paper, we construct a mixed-base number system over the generalized symmetric group G(m, 1, n), which is a complex reflection group with a root system of type B(m) n . We also establish one-to-one correspondence between all positive integers in the set {1, center dot center dot center dot, mnn!} and the elements of G(m, 1, n) by constructing the subexceedant function in relation to this group. In addition, we provide a new enumeration system for G(m, 1, n) by defining the inversion statistic on G(m, 1, n). Finally, we prove that the flag-major index is equi-distributed with this inversion statistic on G(m, 1, n). Therefore, the flag-major index is a Mahonian statistic on G(m, 1, n) with respect to the length function L. (c) 2023 Elsevier Inc. All rights reserved.