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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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