Characterization of quasirandom permutations by a pattern sum

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Authors	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
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.
Related projects:	MUNI AWARD in Science and Humanitites 1