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Barrier Log-Concavity of Large Forests — arXiv:2610.22098

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.22098
License (as archived): CC0-1.0
Archived: 2026-10-16T10:32:48.531Z
SHA-256 of the archived text: a3abc39bcd40444b1cdc0f9784b2bbc93d5e0e91714cfbb153d8d4c7dafd8517
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How to cite

Barrier Log-Concavity of Large Forests — arXiv:2610.22098 — arXiv (en), https://arxiv.org/abs/2610.22098 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_85f9debfd1cd (Metraipolis archive dc_85f9debfd1cd, sha256 a3abc39bcd40444b1cdc0f9784b2bbc93d5e0e91714cfbb153d8d4c7dafd8517)

BibTeX

@misc{dc85f9debfd1cd,
  title = {Barrier Log-Concavity of Large Forests — arXiv:2610.22098},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.22098},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_85f9debfd1cd; sha256 a3abc39bcd40444b1cdc0f9784b2bbc93d5e0e91714cfbb153d8d4c7dafd8517},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.22098. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We prove that the independence sequence of every sufficiently large forest is strictly barrier log-concave: whenever $i_{k+1}>i_k$, one has $i_k^2>i_{k-1}i_{k+1}$. Consequently, every common downward coefficient tilt is unimodal, with one order threshold valid simultaneously for all $0<t\le1$. As an application, we prove that every sufficiently large well-covered tree has a strictly log-concave independence polynomial. More generally, the latter conclusion holds for well-covered forests with sufficiently large matching number. Every sufficiently large forest with a palindromic independence polynomial is also strictly log-concave, with its modes at the central ranks. The proof establishes local coefficient-curvature estimates uniformly over forests of unbounded maximum degree and over activities tending to zero. Combined with the fixed-density theorem of Fang, Lu, Nevo, Yao, and Zheng, these estimates complete the strict log-concavity interval down to rank one through $\lfloor17\alpha/25\rfloor$; the terminal fraction is inherited. The classical decreasing tail then yields the barrier property. A cumulative-coefficient corona theorem transfers barrier log-concavity of the base forest to full strict log-concavity of its leaf corona.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.PR, nuovi lavori del giorno).
Categorie arXiv: Combinatorics (math.CO) ; Discrete Mathematics (cs.DM); Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2610.22098 — 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 2026-10-16T08:50:17.605Z dalla pagina https://arxiv.org/list/math.PR/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).