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Long Lattice Paths with No Three Collinear Vertices — arXiv:2608.07906

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.07906
License (as archived): CC0-1.0
Archived: 2026-10-19T09:08:49.547Z
SHA-256 of the archived text: 6af6664f42adde5ca7cf0cc07710a93615b38063dfe95131ca26477eb92e04c6
Stable URL of this page: https://metraipolis.com/documento/dc_76eaec71c480

How to cite

Long Lattice Paths with No Three Collinear Vertices — arXiv:2608.07906 — arXiv (en), https://arxiv.org/abs/2608.07906 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_76eaec71c480 (Metraipolis archive dc_76eaec71c480, sha256 6af6664f42adde5ca7cf0cc07710a93615b38063dfe95131ca26477eb92e04c6)

BibTeX

@misc{dc76eaec71c480,
  title = {Long Lattice Paths with No Three Collinear Vertices — arXiv:2608.07906},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.07906},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_76eaec71c480; sha256 6af6664f42adde5ca7cf0cc07710a93615b38063dfe95131ca26477eb92e04c6},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.07906. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

For $d\ge 1$, let $L(d)\in\mathbb N\cup\{\infty\}$ be the supremum of the lengths of paths in $\mathbb Z^d$ whose steps are standard basis vectors and whose vertex sets contain no collinear triple. We prove that \[ \log_2\log_2 L(d)\ge \frac{2}{5}d-O(1) \] for all sufficiently large $d$.

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/2608.07906 — 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 2026-10-19T09:05:33.545Z 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).