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Decreasing Runs in Quasi-Stirling Permutations of Multisets — arXiv:2608.09599

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.09599
License (as archived): CC0-1.0
Archived: 2026-10-19T09:09:03.507Z
SHA-256 of the archived text: dd5b2fc991a80c2de7965244446e4ecdeedba4e9595897aa4d7597e2830c6d8b
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How to cite

Decreasing Runs in Quasi-Stirling Permutations of Multisets — arXiv:2608.09599 — arXiv (en), https://arxiv.org/abs/2608.09599 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_afbbcde0ea87 (Metraipolis archive dc_afbbcde0ea87, sha256 dd5b2fc991a80c2de7965244446e4ecdeedba4e9595897aa4d7597e2830c6d8b)

BibTeX

@misc{dcafbbcde0ea87,
  title = {Decreasing Runs in Quasi-Stirling Permutations of Multisets — arXiv:2608.09599},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.09599},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_afbbcde0ea87; sha256 dd5b2fc991a80c2de7965244446e4ecdeedba4e9595897aa4d7597e2830c6d8b},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.09599. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

As a natural extension of Stirling permutations, quasi-Stirling permutations are multipermutations $\pi$ with the property that for any subsequence $\pi_{j_1}\pi_{j_2}\pi_{j_3}\pi_{j_4}$ satisfying $\pi_{j_1}=\pi_{j_3}$ and $\pi_{j_2}=\pi_{j_4}$, we have $\pi_{j_1}=\pi_{j_2}$. Using a bijective construction, Yan, Yang, Huang and Zhu showed that the joint distribution of ascents, descents and plateaux over quasi-Stirling permutations of a multiset $M=\{1^{k_1},2^{k_2},\ldots,n^{k_n}\}$ coincides with that over the multiset $M'=\{1^{k_1+\cdots+k_n-n+1},2,\ldots,n\}$. In this paper, we prove that the same invariance of distribution holds for decreasing runs, and consequently for all decreasing consecutive patterns. To this end, following the Yan-Yang-Huang-Zhu approach, we construct a multiplicity-redistribution bijection that preserves decreasing runs, thereby reducing the computation of joint distribution of decreasing consecutive patterns over quasi-Stirling permutations from $M$ to $M'$. Together with the classical run theorem, our bijection leads to explicit recurrence relations and generating functions for the distribution functions of these statistics over quasi-Stirling permutations.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-11 in math.CO).
Categorie arXiv: Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2608.09599 — 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 2026-10-19T09:05:33.585Z dalla pagina https://arxiv.org/catchup/math.CO/2026-08-11?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).