Year: 2026
Type: preprint
Abstract: We establish Jacobi-type continued fraction expansions for (p,q)-analogues of the bi-Stirling Eulerian polynomials, which refine classical Eulerian statistics on permutations. These polynomials admit equivalent definitions in terms of descents or excedances. The parameters p and q encode refined permutation statistics, including (ldes,rasc) and (cros,nest). Our approach is based on weighted Motzkin path models arising from variants of the bijections of Françon--Viennot and Foata--Zeilberger. As applications, we obtain new results on total positivity and gamma-positivity for several families of enumerative polynomials. Our results unify and extend a number of recent works in the literature.
Source: arXiv (Cornell University)
Authors: Xu, Chao, Zeng, Jiang
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: China Scholarship Council
Award: G8615355325
OpenAlex ID: W7213233157