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Arrangement of hyperplanes — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Arrangement_of_hyperplanes
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-15T14:23:59.098Z
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Arrangement of hyperplanes — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Arrangement_of_hyperplanes (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_f706d30c759d (Metraipolis archive dc_f706d30c759d, sha256 a93da1d4c21e0cf6a5eb48588bc3fba98b751a1926dc0bda7673ee7c194434aa)

BibTeX

@misc{dcf706d30c759d,
  title = {Arrangement of hyperplanes — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Arrangement_of_hyperplanes},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_f706d30c759d; sha256 a93da1d4c21e0cf6a5eb48588bc3fba98b751a1926dc0bda7673ee7c194434aa},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Arrangement_of_hyperplanes. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In geometry and combinatorics, an arrangement of hyperplanes is an arrangement of a finite set A of hyperplanes in a linear, affine, or projective space S. Questions about a hyperplane arrangement A generally concern geometrical, topological, or other properties of the complement, M(A), which is the set that remains when the hyperplanes are removed from the whole space. One may ask how these properties are related to the arrangement and its intersection semilattice. The intersection semilattice of A, written L(A), is the set of all subspaces that are obtained by intersecting some of the hyperplanes; among these subspaces are S itself, all the individual hyperplanes, all intersections of pairs of hyperplanes, etc. (excluding, in the affine case, the empty set). These intersection subspaces of A are also called the flats of A. The intersection semilattice L(A) is partially ordered by reverse inclusion. If the whole space S is 2-dimensional, the hyperplanes are lines; such an arrangement is often called an arrangement of lines. Historically, real arrangements of lines were the first arrangements investigated. If S is 3-dimensional one has an arrangement of planes.

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; categoria «Combinatorics»).
Fonte: Wikipedia in inglese, voce «Arrangement of hyperplanes» — https://en.wikipedia.org/wiki/Arrangement_of_hyperplanes
Wikidata Q4795851 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q4795851
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Arrangement_of_hyperplanes?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1362281258, consultata il 2026-10-15T13:53:36.002Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 329705ae898106ed34ae0eb1f33229b734c734a565af68e7fafe06ba818dab13