HTML Microdata document

This HTML5 document contains 32 embedded RDF statements represented using HTML+Microdata notation.

The embedded RDF content will be recognized by any processor of HTML5 Microdata.

Namespace Prefixes

Prefix	IRI
dct	http://purl.org/dc/terms/
yago-res	http://yago-knowledge.org/resource/
dbo	http://dbpedia.org/ontology/
foaf	http://xmlns.com/foaf/0.1/
n15	https://global.dbpedia.org/id/
dbt	http://dbpedia.org/resource/Template:
rdfs	http://www.w3.org/2000/01/rdf-schema#
rdf	http://www.w3.org/1999/02/22-rdf-syntax-ns#
owl	http://www.w3.org/2002/07/owl#
wikipedia-en	http://en.wikipedia.org/wiki/
dbp	http://dbpedia.org/property/
dbc	http://dbpedia.org/resource/Category:
prov	http://www.w3.org/ns/prov#
xsdh	http://www.w3.org/2001/XMLSchema#
wikidata	http://www.wikidata.org/entity/
dbr	http://dbpedia.org/resource/

Statements

Subject Item: dbr:Minkowski's_theorem
dbo:wikiPageWikiLink: dbr:Ehrhart's_volume_conjecture

Subject Item: dbr:Eugène_Ehrhart
dbo:wikiPageWikiLink: dbr:Ehrhart's_volume_conjecture
dbp:knownFor: dbr:Ehrhart's_volume_conjecture
dbo:knownFor: dbr:Ehrhart's_volume_conjecture

Subject Item: dbr:Ehrhart's_volume_conjecture
rdfs:label: Ehrhart's volume conjecture
rdfs:comment: In the geometry of numbers, Ehrhart's volume conjecture gives an upper bound on the volume of a convex body containing only one lattice point in its interior. It is a kind of converse to Minkowski's theorem, which guarantees that a centrally symmetric convex body K must contain a lattice point as soon as its volume exceeds . The conjecture states that a convex body K containing only one lattice point in its interior as its barycenter cannot have volume greater than : Ehrhart proved the conjecture in dimension 2 and in the case of simplices.
dct:subject: dbc:Conjectures dbc:Geometry_of_numbers dbc:Convex_analysis
dbo:wikiPageID: 50521059
dbo:wikiPageRevisionID: 1117677837
dbo:wikiPageWikiLink: dbc:Conjectures dbr:Standard_simplex dbr:Geometry_of_numbers dbr:Minkowski's_theorem dbc:Convex_analysis dbc:Geometry_of_numbers dbr:Center_of_mass dbr:Convex_body
owl:sameAs: wikidata:Q25105334 yago-res:Ehrhart's_volume_conjecture n15:2MktP
dbp:wikiPageUsesTemplate: dbt:Geometry-stub dbt:Citation dbt:Short_description
dbo:abstract: In the geometry of numbers, Ehrhart's volume conjecture gives an upper bound on the volume of a convex body containing only one lattice point in its interior. It is a kind of converse to Minkowski's theorem, which guarantees that a centrally symmetric convex body K must contain a lattice point as soon as its volume exceeds . The conjecture states that a convex body K containing only one lattice point in its interior as its barycenter cannot have volume greater than : Equality is achieved in this inequality when is a copy of the standard simplex in Euclidean n-dimensional space, whose sides are scaled up by a factor of . Equivalently, is congruent to the convex hull of the vectors , and for all . Presented in this manner, the origin is the only lattice point interior to the convex body K. The conjecture, furthermore, asserts that equality is achieved in the above inequality if and only if K is unimodularly equivalent to . Ehrhart proved the conjecture in dimension 2 and in the case of simplices.
prov:wasDerivedFrom: wikipedia-en:Ehrhart's_volume_conjecture?oldid=1117677837&ns=0
dbo:wikiPageLength: 1889
foaf:isPrimaryTopicOf: wikipedia-en:Ehrhart's_volume_conjecture

Subject Item: dbr:Pi
dbo:wikiPageWikiLink: dbr:Ehrhart's_volume_conjecture

Subject Item: dbr:List_of_unsolved_problems_in_mathematics
dbo:wikiPageWikiLink: dbr:Ehrhart's_volume_conjecture

Subject Item: wikipedia-en:Ehrhart's_volume_conjecture
foaf:primaryTopic: dbr:Ehrhart's_volume_conjecture