Publication details

Characterization of quasirandom permutations by a pattern sum


CHAN Timothy F. N. KRÁĽ Daniel NOEL Jonathan A. PEHOVA Yanitsa SHARIFZADEH Maryam VOLEC Jan

Year of publication 2020
Type Article in Periodical
Magazine / Source Random Structures and Algorithms
MU Faculty or unit

Faculty of Informatics

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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