Characterization of quasirandom permutations by a pattern sum
| Authors | |
|---|---|
| Year of publication | 2020 |
| Type | Article in Periodical |
| Magazine / Source | Random Structures and Algorithms |
| MU Faculty or unit | |
| Citation | |
| Web | http://dx.doi.org/10.1002/rsa.20956 |
| Doi | http://dx.doi.org/10.1002/rsa.20956 |
| Keywords | permutations; quasirandomness |
| Description | It is known that a sequence{pi i}i is an element of Nof permutations is quasirandom if and only if the pattern density of every 4-point permutation in pi iconverges to 1/24. We show that there is a setSof 4-point permutations such that the sum of the pattern densities of the permutations fromSin the permutations pi iconverges to|S|/24if and only if the sequence is quasirandom. Moreover, we are able to completely characterize the setsSwith this property. In particular, there are exactly ten such sets, the smallest of which has cardinality eight. |
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