Packings in Real Projective Spaces
نویسندگان
چکیده
منابع مشابه
Packings in real projective spaces
This paper applies techniques from algebraic and differential geometry to determine how to best pack points in real projective spaces. We present a computer-assisted proof of the optimality of a particular 6-packing in RP, we introduce a linear-time constant-factor approximation algorithm for packing in the so-called Gerzon range, and we provide local optimality certificates for two infinite fa...
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The question of finding the smallest Euclidean space in which real projective space P n can be (differentiably) embedded was the subject of intense investigation during the 1960s and 1970s. The purpose of this paper is to survey the status of the question, and add a little bit to our knowledge by proving one new family of embeddings, using old methods of obstruction theory. Our new result is gi...
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This report presents a numerical method for finding good packings on spheres, in projective spaces, and in Grassmannian manifolds equipped with various metrics. In each case, producing a good packing is equivalent to constructing a matrix that has certain structural and spectral properties. By alternately enforcing the structural condition and then the spectral condition, it is frequently possi...
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The computation of the equivariant K-theory K∗ G(V ) of the Thom space of a real vector bundle has been done successfully only under some spinoriality conditions [1], thanks to a clever use of the Atiyah–Singer index theorem (even if G is a finite group). One purpose of this paper is to fill this gap, at least for real vector spaces (considered as vector bundles over a point). For this purpose,...
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ژورنال
عنوان ژورنال: SIAM Journal on Applied Algebra and Geometry
سال: 2018
ISSN: 2470-6566
DOI: 10.1137/17m1137528