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- W3037504706 abstract "Chung and Graham define quasirandom subsets of $mathbb{Z}_n$ to be those with any one of a large collection of equivalent random-like properties. We weaken their definition and call a subset of $mathbb{Z}_n$ $epsilon$-balanced if its discrepancy on each interval is bounded by $epsilon n$. A quasirandom permutation, then, is one which maps each interval to a highly balanced set. In the spirit of previous studies of quasirandomness, we exhibit several random-like properties which are equivalent to this one, including the property of containing (approximately) the expected number of subsequences of each order-type. We provide a few applications of these results, present a construction for a family of strongly quasirandom permutations, and prove that this construction is essentially optimal, using a result of W. Schmidt on the discrepancy of sequences of real numbers." @default.
- W3037504706 created "2020-07-02" @default.
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- W3037504706 date "2002-10-31" @default.
- W3037504706 modified "2023-09-26" @default.
- W3037504706 title "Quasirandom Permutations" @default.
- W3037504706 hasPublicationYear "2002" @default.
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