European Journal of Combinatorics· 2026Q1
Cyclotomic Euler–Mahonian polynomials
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- 2026year
Short summary
A new formula based on the Hadamard product provides the first general results for cyclotomic Euler–Mahonian polynomials, including previously missing odd cases and an I-analogue of Wachs' formula.
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Key points
- Introduces a formula for cyclotomic Euler–Mahonian polynomials using the Hadamard product.
- Provides the first general results for the joint study of these polynomials.
- Derives the I-analogue (I = -1) of Wachs' formula for signed Euler–Mahonian polynomials.
- Completes the study of signed Euler–Mahonian polynomials by providing the odd case.
AI-generated from the title and abstract; the full text is not read.
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.
The authors' abstract, as published at the source. European Journal of Combinatorics, 2026 · DOI ↗
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Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics