Characterization of quasirandom permutations by a pattern sum

Varování

Publikace nespadá pod Fakultu sportovních studií, ale pod Fakultu informatiky. Oficiální stránka publikace je na webu muni.cz.

Autoři	CHAN Timothy F. N. KRÁĽ Daniel NOEL Jonathan A. PEHOVA Yanitsa SHARIFZADEH Maryam VOLEC Jan
Rok publikování	2020
Druh	Článek v odborném periodiku
Časopis / Zdroj	Random Structures and Algorithms
Fakulta / Pracoviště MU	Fakulta informatiky
Citace
www	http://dx.doi.org/10.1002/rsa.20956
Doi	http://dx.doi.org/10.1002/rsa.20956
Klíčová slova	permutations; quasirandomness
Popis	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.
Související projekty:	MUNI AWARD in Science and Humanitites 1