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arXiv math/0501245math.NTmath.CO

Supertopes

Robert Erdahl, Konstantin Rybnikov

备注：
This is a corrected and extended version of a preprint prepared by Rybnikov at the end of 2002. That preprint grew up from the work of Rybnikov and Erdahl in Queen's University at the end of 1990s and Research Experience for Undergraduates Program in Geometry of Numbers directed by Rybnikov in the summer of 2001 in Cornell University, Department of Mathematics. The preprint presents an introduction to the topic of perfect Delaunay polytopes and ellipsoids and reflects the state of knowledge as of October of 2002
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英文摘要：

A perfect (Delaunay) ellipsoid is an ellipsoid in n-dimensional Euclidean space that does not contain integral points in its interior, but is uniquely defined by integral points that lie on its surface. A perfect Delaunay polytope with respect to a positive quadratic form f() is a polytope with integral vertices that is circumscribed by a perfect Delaunay ellipsoid with an equation whose quadratic part is f(). This document has been corrected on January 15, 2005. Note that it represents the state of the area as of the end of 2002. For recent research on perfect Delaunay polytopes see my recent preprint, with Erdahl and Ordine, math.NT/0408122 on ArXiv.org .

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