منابع مشابه
A Doubly Exponentially Crumbled Cake
We consider the following cake cutting game: Alice chooses a set P of n points in the square (cake) [0, 1], where (0, 0) ∈ P ; Bob cuts out n axis-parallel rectangles with disjoint interiors, each of them having a point of P as the lower left corner; Alice keeps the rest. It has been conjectured that Bob can always secure at least half of the cake. This remains unsettled, and it is not even kno...
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Begin with a set of four points in the real plane in general position. Add to this collection the intersection of all lines through pairs of these points. Iterate. Ismailescu and Radoičić (2003) showed that the limiting set is dense in the plane. We give doubly exponential upper and lower bounds on the number of points at each stage. The proof employs a variant of the Szemerédi-Trotter Theorem ...
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In this note we give sharp estimates on the volume of the set of separable states on N qubits. In particular, the magnitude of the “effective radius” of that set in the sense of volume is determined up to a factor which is a (small) power of N , and thus precisely on the scale of powers of its dimension. Similar but less precise results are obtained for qudits. Additionally, one of the appendic...
متن کاملIterated Point - Line Configurations Grow Doubly - Exponentially Joshua Cooper and
Begin with a set of four points in the real plane in general position. Add to this collection the intersection of all lines through pairs of these points. Iterate. Ismailescu and Radoičić (2003) showed that the limiting set is dense in the plane. We give doubly exponential upper and lower bounds on the number of points at each stage. The proof employs a variant of the Szemerédi-Trotter Theorem ...
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From 24.06. to 29.06.2007, the Dagstuhl Seminar 07261 Fair Division was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put to...
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ژورنال
عنوان ژورنال: Electronic Notes in Discrete Mathematics
سال: 2011
ISSN: 1571-0653
DOI: 10.1016/j.endm.2011.09.044