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- W3100509900 abstract "A set $S$ of permutations is forcing if for any sequence ${Pi_i}_{i in mathbb{N}}$ of permutations where the density $d(pi,Pi_i)$ converges to $frac{1}{|pi|!}$ for every permutation $pi in S$, it holds that ${Pi_i}_{i in mathbb{N}}$ 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 $kge 4$. In particular, the set of all twenty-four 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." @default.
- W3100509900 created "2020-11-23" @default.
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- W3100509900 date "2020-11-18" @default.
- W3100509900 modified "2023-09-27" @default.
- W3100509900 title "Lower bound on the size of a quasirandom forcing set of permutations" @default.
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