Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 36 min ago
PreprintarXiv licencearXiv

The (p,q)-Analogues of Bi-Stirling Eulerian Polynomials via continued fractions

  • Chao Xu
  • Jiang Zeng
Open at sourcePDFDOICite

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.

Related

  1. The q-analogues of γ-positivity of Eulerian polynomials via group actions
    Taifeng Ding, Lintong Wang, Sherry H. F. Yan
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv
  2. An elementary treatment of Ramanujan's elementary continued fractions
    Gaurav Bhatnagar
    arXivPreprintCC BY-SA 4.0Full textAlgebra & number theoryAnalysis & PDEsarXiv
  3. Weak Hurwitz stability of extended Turán expressions for Stirling--Whitney--Riordan and Laguerre polynomials
    Wenle Shi
    arXivPreprintarXiv licenceFull textAnalysis & PDEsCombinatorics & discrete mathematicsarXiv
  4. Binomial expansions of Jacobi-Stirling numbers and real-rootedness of Jacobi-Stirling descent polynomials
    Shi-Mei Ma, Ming-Xin Wang
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  5. Continued Fractions of Polynomial Type: Theory and Encyclopedic Dictionary
    Henri Cohen
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{xu2026pqanalogues,
  title = {{The (p,q)-Analogues of Bi-Stirling Eulerian Polynomials via continued fractions}},
  author = {Chao Xu and Jiang Zeng},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14386},
  eprint = {2609.14386},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14386},
}
RIS
TY  - UNPB
TI  - The (p,q)-Analogues of Bi-Stirling Eulerian Polynomials via continued fractions
AU  - Chao Xu
AU  - Jiang Zeng
PY  - 2026
DA  - 2026/09/13
PB  - arXiv
DO  - 10.48550/arxiv.2609.14386
UR  - https://arxiv.org/abs/2609.14386
AB  - 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.
ER  -