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@article{1799708, author = {Kurečka, Martin}, article_number = {2}, doi = {http://dx.doi.org/10.1017/S0963548321000298}, keywords = {quasirandomness; quasirandom permutations; combinatorial limits; quasirandomness forcing}, language = {eng}, issn = {0963-5483}, journal = {COMBINATORICS PROBABILITY & COMPUTING}, title = {Lower bound on the size of a quasirandom forcing set of permutations}, url = {http://dx.doi.org/10.1017/S0963548321000298}, volume = {31}, year = {2022} }
TY - JOUR ID - 1799708 AU - Kurečka, Martin PY - 2022 TI - Lower bound on the size of a quasirandom forcing set of permutations JF - COMBINATORICS PROBABILITY & COMPUTING VL - 31 IS - 2 SP - 304-319 EP - 304-319 SN - 09635483 KW - quasirandomness KW - quasirandom permutations KW - combinatorial limits KW - quasirandomness forcing UR - http://dx.doi.org/10.1017/S0963548321000298 N2 - A set S of permutations is forcing if for any sequence {Pi_i} of permutations where the density d(pi, Pi_i) converges to 1/|pi|! for every permutation pi from S, it holds that {Pi_i} is quasirandom. Graham asked whether there exists an integer k such that the set of all permutations of order k is forcing; this has been shown to be true for any k>=4 . In particular, the set of all 24 permutations of order 4 is forcing. We provide the first non-trivial lower bound on the size of a forcing set of permutations: every forcing set of permutations (with arbitrary orders) contains at least four permutations. ER -
KUREČKA, Martin. Lower bound on the size of a quasirandom forcing set of permutations. \textit{COMBINATORICS PROBABILITY \&{} COMPUTING}. 2022, roč.~31, č.~2, s.~304-319. ISSN~0963-5483. Dostupné z: https://dx.doi.org/10.1017/S0963548321000298.
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