Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:automorphismGroup |
projective linear group
|
| gptkbp:definedIn |
finite fields
|
| gptkbp:dimensions |
n-dimensional
|
| gptkbp:example |
gptkb:Fano_plane
|
| gptkbp:field |
gptkb:geometry
combinatorics |
| gptkbp:generalizes |
projective planes
|
| gptkbp:has_lines |
finite set
|
| gptkbp:has_points |
finite set
|
| https://www.w3.org/2000/01/rdf-schema#label |
finite projective spaces
|
| gptkbp:notation |
PG(n,q)
|
| gptkbp:number_of_lines_in_PG(2,q) |
q^2+q+1
|
| gptkbp:number_of_points_in_PG(n,q) |
(q^{n+1}-1)/(q-1)
|
| gptkbp:order |
q (a prime power)
|
| gptkbp:property |
homogeneous coordinates
no parallel lines any two distinct lines meet in a unique point any two distinct points determine a unique line duality principle applies every line contains q+1 points every point lies on q+1 lines |
| gptkbp:relatedTo |
gptkb:geometry
gptkb:Galois_fields incidence structures block designs |
| gptkbp:studiedBy |
gptkb:geometry
|
| gptkbp:used_in |
coding theory
design theory finite group theory |
| gptkbp:bfsParent |
gptkb:Bose–Burton_theorem
|
| gptkbp:bfsLayer |
8
|