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Multivariate stability of powered triangular recurrences and parametrised Eulerian polynomials — arXiv:2609.15651

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.15651
License (as archived): CC0-1.0
Archived: 2026-10-16T01:25:32.253Z
SHA-256 of the archived text: 0b646eaceb66c43c573b992ae8cf0f742a69abcb61b408d1c3b2a69adf6c7995
Stable URL of this page: https://metraipolis.com/documento/dc_7be8cbfaecce

How to cite

Multivariate stability of powered triangular recurrences and parametrised Eulerian polynomials — arXiv:2609.15651 — arXiv (en), https://arxiv.org/abs/2609.15651 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_7be8cbfaecce (Metraipolis archive dc_7be8cbfaecce, sha256 0b646eaceb66c43c573b992ae8cf0f742a69abcb61b408d1c3b2a69adf6c7995)

BibTeX

@misc{dc7be8cbfaecce,
  title = {Multivariate stability of powered triangular recurrences and parametrised Eulerian polynomials — arXiv:2609.15651},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.15651},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_7be8cbfaecce; sha256 0b646eaceb66c43c573b992ae8cf0f742a69abcb61b408d1c3b2a69adf6c7995},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.15651. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We prove multivariate stability for a class of affine triangular recurrences whose two coefficients are raised to an arbitrary positive integer power. The variables keep track of cross-step heights in a weighted lattice-path model. The applications include stability and real rootedness of parametrised Eulerian, Stirling, and Lah families. For the parametrised Eulerian polynomials, we obtain multivariate refinements of known real-rootedness results and prove simplicity and strict interlacing of consecutive rows. A kernel-preserving bijection with increasing binary trees yields a synchronised Foata--Strehl action on pairs and a combinatorial interpretation of their gamma coefficients along with a recurrence. The same bijection identifies refinement posets that admit symmetric Boolean and chain decompositions for parameter one and cover-supported $\mathfrak{sl}_2$ operators prove their PECKness. We extend the stability and strict interlacing results to synchronised Stirling permutations and prove PECKness for ordinary Stirling permutations with a fixed number of plateaux.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-15 in math.CO).
Categorie arXiv: Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2609.15651 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T00:39:30.250Z dalla pagina https://arxiv.org/catchup/math.CO/2026-09-15?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).