Quasirandom Permutations
| dc.creator | Cooper, Joshua N. | |
| dc.date | 2002-10-31 | |
| dc.date.accessioned | 2026-07-07T04:52:32Z | |
| dc.date.available | 2026-07-07T04:52:32Z | |
| dc.description | 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 $\mathbb{Z}_n$ $ε$-balanced if its discrepancy on each interval is bounded by $εn$. 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. | |
| dc.description | 30 pages, 2 figures, submitted to JCTA | |
| dc.identifier | https://arxiv.org/abs/math/0211001 | |
| dc.identifier | http://arxiv.org/abs/math/0211001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65500 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 05D40; 11K45 | |
| dc.title | Quasirandom Permutations | |
| dc.type | text |