CHAN, Timothy F. N., Daniel KRÁĽ, Jonathan A. NOEL, Yanitsa PEHOVA, Maryam SHARIFZADEH and Jan VOLEC. Characterization of quasirandom permutations by a pattern sum. Random Structures and Algorithms. HOBOKEN: WILEY, 2020, vol. 57, No 4, p. 920-939. ISSN 1042-9832. Available from: https://dx.doi.org/10.1002/rsa.20956. |
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@article{1759843, author = {Chan, Timothy F. N. and Kráľ, Daniel and Noel, Jonathan A. and Pehova, Yanitsa and Sharifzadeh, Maryam and Volec, Jan}, article_location = {HOBOKEN}, article_number = {4}, doi = {http://dx.doi.org/10.1002/rsa.20956}, keywords = {permutations; quasirandomness}, language = {eng}, issn = {1042-9832}, journal = {Random Structures and Algorithms}, title = {Characterization of quasirandom permutations by a pattern sum}, url = {http://dx.doi.org/10.1002/rsa.20956}, volume = {57}, year = {2020} }
TY - JOUR ID - 1759843 AU - Chan, Timothy F. N. - Kráľ, Daniel - Noel, Jonathan A. - Pehova, Yanitsa - Sharifzadeh, Maryam - Volec, Jan PY - 2020 TI - Characterization of quasirandom permutations by a pattern sum JF - Random Structures and Algorithms VL - 57 IS - 4 SP - 920-939 EP - 920-939 PB - WILEY SN - 10429832 KW - permutations KW - quasirandomness UR - http://dx.doi.org/10.1002/rsa.20956 N2 - 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. ER -
CHAN, Timothy F. N., Daniel KRÁĽ, Jonathan A. NOEL, Yanitsa PEHOVA, Maryam SHARIFZADEH and Jan VOLEC. Characterization of quasirandom permutations by a pattern sum. \textit{Random Structures and Algorithms}. HOBOKEN: WILEY, 2020, vol.~57, No~4, p.~920-939. ISSN~1042-9832. Available from: https://dx.doi.org/10.1002/rsa.20956.
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