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A colorful Steinitz theorem with different centers — arXiv:2609.21927

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.21927
License (as archived): CC0-1.0
Archived: 2026-10-10T02:12:42.306Z
SHA-256 of the archived text: 40747090723296442cff306b78a164b702ae80d9399188fc7c1b7d361d4decc3
Stable URL of this page: https://metraipolis.com/documento/dc_283d20105978

How to cite

A colorful Steinitz theorem with different centers — arXiv:2609.21927 — arXiv (en), https://arxiv.org/abs/2609.21927 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_283d20105978 (Metraipolis archive dc_283d20105978, sha256 40747090723296442cff306b78a164b702ae80d9399188fc7c1b7d361d4decc3)

BibTeX

@misc{dc283d20105978,
  title = {A colorful Steinitz theorem with different centers — arXiv:2609.21927},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.21927},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_283d20105978; sha256 40747090723296442cff306b78a164b702ae80d9399188fc7c1b7d361d4decc3},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.21927. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We prove a colorful quantitative Steinitz theorem in which the color classes may have different centers. If the convex hull of each of $2d$ sets in $\R^d$ contains a translate of the Euclidean unit ball, then a rainbow convex hull contains a ball of radius $(3d)^{-2d^2}$ whose center belongs to the convex hull of the given centers. The main ingredient is an exact result for translates of a segment, proved by a lifting and a topological colorful Helly theorem. The same idea also yields a sharp colorful Helly theorem for translated cones: for $1 \le k \le d-1$, if every rainbow selection from $2d-k+1$ finite families of convex sets in $\mathbb{R}^d$ has a $k$-dimensional cone in its intersection, then the intersection of one of the families contains such a cone.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-21 in math.CO).
Categorie arXiv: Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2609.21927 — 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 2026-10-10T01:48:20.608Z dalla pagina https://arxiv.org/catchup/math.CO/2026-09-21?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).