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$k$-arrangements of pseudolines and pseudocircles — arXiv:2610.00773

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.00773
License (as archived): CC0-1.0
Archived: 2026-10-06T17:40:42.204Z
SHA-256 of the archived text: 3242fef1fa01e512a61214ab1f5b5b373d885cb8063c087f093807208262ef66
Stable URL of this page: https://metraipolis.com/documento/dc_0eaafdce8aca

How to cite

$k$-arrangements of pseudolines and pseudocircles — arXiv:2610.00773 — arXiv (en), https://arxiv.org/abs/2610.00773 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_0eaafdce8aca (Metraipolis archive dc_0eaafdce8aca, sha256 3242fef1fa01e512a61214ab1f5b5b373d885cb8063c087f093807208262ef66)

BibTeX

@misc{dc0eaafdce8aca,
  title = {$k$-arrangements of pseudolines and pseudocircles — arXiv:2610.00773},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.00773},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_0eaafdce8aca; sha256 3242fef1fa01e512a61214ab1f5b5b373d885cb8063c087f093807208262ef66},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.00773. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

A $k$-arrangement of pseudolines is a set of bi-infinite curves in the plane such that any two of them intersect each other in exactly $k$ points, at which they cross, and it is simple if no three curves meet at a common point. Cyclic arrangements are the only simple $1$-arrangements of pseudolines that are unavoidable, in the Ramsey spirit: for each fixed $m\ge 1$, every sufficiently large simple $1$-arrangement of pseudolines has a cyclic subarrangement of size $m$. We show that, for every $m\ge 3$, the number of unavoidable simple $k$-arrangements of pseudolines of size $m$ grows exponentially with $k$, independently of $m$. For even $k$, we prove an analogous result for $k$-arrangements of pseudocircles.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-10-02 in math.CO).
Categorie arXiv: Combinatorics (math.CO) ; Computational Geometry (cs.CG).
Pagina del lavoro: https://arxiv.org/abs/2610.00773 — 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 2026-10-06T16:06:55.821Z dalla pagina https://arxiv.org/catchup/math.CO/2026-10-02?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).