TY - JOUR
T1 - Signed Euler–Mahonian identities
AU - Eu, Sen Peng
AU - Lin, Zhicong
AU - Lo, Yuan Hsun
N1 - Funding Information:
The authors would like to express their gratitude to the referees for their valuable comments and suggestions on improving the presentation of this paper. This research is partially supported by Ministry of Science and Technology, Taiwan under Grants 107-2115-M-003-009-MY3 (S.-P. Eu) and 108-2115-M-153-004-MY2 (Y.-H. Lo), the National Natural Science Foundation of China under Grant 11871247 (Z. Lin), and the project of Qilu Young Scholars of Shandong University (Z. Lin).
Publisher Copyright:
© 2020 Elsevier Ltd
PY - 2021/1
Y1 - 2021/1
N2 - A relationship between signed Eulerian polynomials and the classical Eulerian polynomials on Sn was given by Désarménien and Foata in 1992, and a refined version, called signed Euler–Mahonian identity, together with a bijective proof was 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 Bn, Dn, 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 Bn and Dn.
AB - A relationship between signed Eulerian polynomials and the classical Eulerian polynomials on Sn was given by Désarménien and Foata in 1992, and a refined version, called signed Euler–Mahonian identity, together with a bijective proof was 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 Bn, Dn, 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 Bn and Dn.
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U2 - 10.1016/j.ejc.2020.103209
DO - 10.1016/j.ejc.2020.103209
M3 - Article
AN - SCOPUS:85090130814
SN - 0195-6698
VL - 91
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
M1 - 103209
ER -