Cyclotomic Euler–Mahonian polynomials
Abstract
The cyclotomic Eulerian polynomials and the cyclotomic Mahonian polynomials have each been the subject of extensive studies in Combinatorics, with particular attention to their signed versions. In contrast, the joint study of cyclotomic Euler-Mahonian polynomials has received far less consideration. To the best of our knowledge, the only prior result in this direction is a formula due to Wachs for the signed Euler-Mahonian polynomials in the even case. In this paper, we focus on the cyclotomic Euler-Mahonian polynomials and derive a formula based on the Hadamard product. As corollaries, we obtain the I-analogue (where I = √ -1) of Wachs' formula for signed Euler-Mahonian polynomials, as well as the previously missing odd case for the signed Euler-Mahonian polynomials.
Related
- Post-critically finite polynomials over cyclotomic closures of number fields
- Cyclotomic polynomials with trinomial irreducible factors over finite fields
- Rectangular Cyclotomic Expansions of Colored HOMFLY-PT Polynomials
- Invariant factors from products of cyclotomic polynomials, with applications
- SIC dimension towers via cyclotomic polynomials
BibTeX
@article{han2026cyclotomic,
title = {{Cyclotomic Euler–Mahonian polynomials}},
author = {Guo-Niu Han},
journal = {European Journal of Combinatorics},
year = {2026},
month = oct,
doi = {10.1016/j.ejc.2026.104455},
url = {https://cnrs.hal.science/hal-05839111v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - JOUR
TI - Cyclotomic Euler–Mahonian polynomials
AU - Guo-Niu Han
PY - 2026
DA - 2026/10/26
JO - European Journal of Combinatorics
DO - 10.1016/j.ejc.2026.104455
UR - https://cnrs.hal.science/hal-05839111v1
AB - The cyclotomic Eulerian polynomials and the cyclotomic Mahonian polynomials have each been the subject of extensive studies in Combinatorics, with particular attention to their signed versions. In contrast, the joint study of cyclotomic Euler-Mahonian polynomials has received far less consideration. To the best of our knowledge, the only prior result in this direction is a formula due to Wachs for the signed Euler-Mahonian polynomials in the even case. In this paper, we focus on the cyclotomic Euler-Mahonian polynomials and derive a formula based on the Hadamard product. As corollaries, we obtain the I-analogue (where I = √ -1) of Wachs' formula for signed Euler-Mahonian polynomials, as well as the previously missing odd case for the signed Euler-Mahonian polynomials.
SN - 0195-6698
SN - 1095-9971
ER -