A bi-Stirling-Euler-Mahonian polynomial

2025/09/02 by Chao Xu, Jiang Zeng, Xu, Chao +1
Mathematics · #05A05 #05A15 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2509.02461

openalex publication_date 2025/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Motivated by recent work on (re)mixed Eulerian numbers, we provide a combinatorial interpretation of a subfamily of the remixed Eulerian numbers introduced by Nadeau and Tewari. More specifically, we show that these numbers can be realized as the generating polynomials of permutations with respect to the statistics of left-to-right minima, right-to-left minima, descents, and the mixed major index. Our results generalize both the bi-Stirling-Eulerian polynomials of Carlitz-Scoville and the Stirling-Euler-Mahonian polynomials of Butler.

Citations

• Remixed Eulerian numbers: beyond the connected case
• A q-analog of the Stirling-Eulerian Polynomials
• Remixed Eulerian numbers
• A q-deformation of an algebra of Klyachko and Macdonald's reduced word formula
• Théorie Géométrique des Polynômes Eulériens
• Permutohedra, associahedra, and beyond

Related

• Symmetric decompositions and Euler-Stirling statistics on Stirling permutations
• Euler-Mahonian polynomials for C_a \wr S_n
• The Binomial-Stirling-Eulerian Polynomials
• The (α,β)-Eulerian Polynomials and Descent-Stirling Statistics on Permutations
• Eulerian polynomials, Stirling permutations and increasing trees