A frequently studied problem in discrete geometry is to identify ways in which an object can be covered by other simpler objects such as points, lines, and planes. In projective geometry, a specific instance of this problem that has numerous applications is determining whether, and how, a projective space can be covered by pairwise disjoint subspaces which have the same dimension; such a partition is called a spread. Specifically, a spread of a projective space , where is an integer and a division ring, is a set of -dimensional subspaces, for some such that every point of the space lies in exactly one of the elements of the spread.
Attributes | Values |
---|
rdfs:label
| - Spread (projective geometry) (en)
|
rdfs:comment
| - A frequently studied problem in discrete geometry is to identify ways in which an object can be covered by other simpler objects such as points, lines, and planes. In projective geometry, a specific instance of this problem that has numerous applications is determining whether, and how, a projective space can be covered by pairwise disjoint subspaces which have the same dimension; such a partition is called a spread. Specifically, a spread of a projective space , where is an integer and a division ring, is a set of -dimensional subspaces, for some such that every point of the space lies in exactly one of the elements of the spread. (en)
|
dcterms:subject
| |
Wikipage page ID
| |
Wikipage revision ID
| |
Link from a Wikipage to another Wikipage
| |
sameAs
| |
dbp:wikiPageUsesTemplate
| |
has abstract
| - A frequently studied problem in discrete geometry is to identify ways in which an object can be covered by other simpler objects such as points, lines, and planes. In projective geometry, a specific instance of this problem that has numerous applications is determining whether, and how, a projective space can be covered by pairwise disjoint subspaces which have the same dimension; such a partition is called a spread. Specifically, a spread of a projective space , where is an integer and a division ring, is a set of -dimensional subspaces, for some such that every point of the space lies in exactly one of the elements of the spread. Spreads are particularly well-studied in projective geometries over finite fields, though some notable results apply to infinite projective geometries as well. In the finite case, the foundational work on spreads appears in André and independently in Bruck-Bose in connection with the theory of translation planes. In these papers, it is shown that a spread of -dimensional subspaces of the finite projective space exists if and only if . (en)
|
prov:wasDerivedFrom
| |
page length (characters) of wiki page
| |
foaf:isPrimaryTopicOf
| |
is Link from a Wikipage to another Wikipage
of | |
is foaf:primaryTopic
of | |