Forcing quasirandomness with 4-point permutations
<|reference_start|>Forcing quasirandomness with 4-point permutations: A combinatorial object is said to be quasirandom if it exhibits certain properties that are typically seen in a truly random object of the same kind. It is known that a permutation is quasirandom if and only if the pattern density of each of the twenty-four 4-point permutations is close to 1/24, which is its expected value in a random permutation. In other words, the set of all twenty-four 4-point permutations is quasirandom-forcing. Moreover, it is known that there exist sets of eight 4-point permutations that are also quasirandom-forcing. Breaking the barrier of linear dependency of perturbation gradients, we show that every quasirandom-forcing set of 4-point permutations must have cardinality at least five.<|reference_end|>
@article{kráľ2024forcing,
    title={Forcing quasirandomness with 4-point permutations},
    author={Daniel Kr'av{l} and Jae-baek Lee and Jonathan A. Noel},
    journal={arXiv preprint arXiv:2407.06869},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.06869},
    primaryClass={math.CO cs.DM}
}