منابع مشابه
Empty Monochromatic Simplices
Let S be a k-colored (finite) set of n points in R, d ≥ 3, in general position, that is, no (d+1) points of S lie in a common (d−1)-dimensional hyperplane. We count the number of empty monochromatic d-simplices determined by S, that is, simplices which have only points from one color class of S as vertices and no points of S in their interior. For 3 ≤ k ≤ d we provide a lower bound of Ω(nd−k+1+...
متن کاملSimplices in the Euclidean ball
We establish some inequalities for the second moment 1 |K| Z
متن کاملOn Empty Lattice Simplices in Dimension 4
We give an almost complete classification of empty lattice simplices in dimension 4 using the conjectural results of Mori-Morrison-Morrison, later proved by Sankaran and Bober. In particular, all of these simplices correspond to cyclic quotient singularities, and all but finitely many of them have width bounded by 2.
متن کاملAn Introduction to Empty Lattice Simplices
We study simplices whose vertices lie on a lattice and have no other lattice points. Suchèmpty lattice simplices' come up in the theory of integer programming, and in some combi-natorial problems. They have been investigated in various contexts and under varying terminology Can thèemptiness' of lattice simplices bèwell-characterized' ? Is theirìattice-width' small ? Do the integer points of the...
متن کاملEuclidean simplices generating discrete reflection groups
Let P be a convex polytope in the spherical space S, in the Euclidean space E, or in the hyperbolic space H. Consider the group GP generated by reflections in the facets of P . We call GP a reflection group generated by P . The problem we consider in this paper is to list polytopes generating discrete reflection groups. The answer is known only for some combinatorial types of polytopes. Already...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Canadian Mathematical Bulletin
سال: 1987
ISSN: 0008-4395,1496-4287
DOI: 10.4153/cmb-1987-064-1