Using permutations to reduce discrepancy
نویسندگان
چکیده
منابع مشابه
Using Rademacher Permutations to Reduce Randomness
It is shown how a special family of unitary operators, called the Rademacher permutations and related to the Clifford algebra, can be used to reduce the level of randomness in several results in asymptotic geometric analysis. §
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On the one hand, random permutations appear as a natural model for data in various topics, such as analysis of algorithms, statistical mechanics, or genomic statistics. On the other hand, from the mathematical point of view, various parameters of random permutations have been studied in combinatorics and probability, like the distribution of the lengths of cycles, the repartition of the eigenva...
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Given three permutations on the integers 1 through n, consider the set system consisting of each interval in each of the three permutations. József Beck conjectured (c. 1987) that the discrepancy of this set system is O(1). We give a counterexample to this conjecture: for any positive integer n = 3, we exhibit three permutations whose corresponding set system has discrepancy Ω(logn). Our counte...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1990
ISSN: 0377-0427
DOI: 10.1016/0377-0427(90)90340-6