A GEOMETRIC HALL-TYPE THEOREM

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We introduce a geometric generalization of Hall's marriage theorem. For any family F = {X-1,...,X-m} of finite sets in R-d, we give conditions under which it is possible to choose a point x(i# is an element of X-i for every 1 <= i <= m in such a way that the points {x#1#,..., x#m)} subset of R-d are in general position. We give two proofs, one elementary proof requiring slightly stronger conditions, and one proof using topological techniques in the spirit of Aharoni and Haxell's celebrated generalization of Hall's theorem.
Publisher
AMER MATHEMATICAL SOC
Issue Date
2016-02
Language
English
Article Type
Article
Keywords

COMPLEXES; HOMOLOGY; GRAPHS

Citation

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, v.144, no.2, pp.503 - 511

ISSN
0002-9939
DOI
10.1090/proc12733
URI
http://hdl.handle.net/10203/205484
Appears in Collection
MA-Journal Papers(저널논문)
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