A point in a $$nd$$ n d -polytope is the barycenter of $$n$$ n points in its $$d$$ d -faces

Autor:	Michael Gene Dobbins
Rok vydání:	2014
Předmět:	Combinatorics Equivariant topology Conjecture General Mathematics Convex polytope Mathematics::Metric Geometry Point (geometry) Polytope Center of mass Skeleton (category theory) Minkowski addition Mathematics
Zdroj:	Inventiones mathematicae. 199:287-292
ISSN:	1432-1297 0020-9910
DOI:	10.1007/s00222-014-0523-2
Popis:	Using equivariant topology, we prove that it is always possible to find $$n$$ points in the $$d$$ -dimensional faces of a $$nd$$ -dimensional convex polytope $$P$$ so that their center of mass is a target point in $$P$$ . Equivalently, the $$n$$ -fold Minkowski sum of a $$nd$$ -polytope’s $$d$$ -skeleton is that polytope scaled by $$n$$ . This verifies a conjecture by Takeshi Tokuyama.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::5e90a754bcaaa7a79a1f660777b416da https://doi.org/10.1007/s00222-014-0523-2 Zobrazit plný text záznamu Full text from SpringerLink