A341299 - OEIS

%I #15 Apr 05 2021 20:58:07

%S 1,3,7,13,20,28,36,48

%N a(n) = least integer m such that at least half of all permutations of length m contain subsequences order isomorphic to every permutation of length n.

%C Engen-Vatter say these values are "suggested", so presumably they have not yet been confirmed.

%H R. Arratia, <a href="https://doi.org/10.37236/1477">On the Stanley-Wilf conjecture for the number of permutations avoiding a given pattern.</a>, Electron. J. Combin. 6, N1 (1999).

%H Michael Engen and Vincent Vatter, <a href="https://doi.org/10.1080/00029890.2021.1835384">Containing all permutations</a>, Amer. Math. Monthly, 128 (2021), 4-24; <a href="https://arxiv.org/abs/1810.08252">arXiv preprint</a>, arXiv:1810.08252 [math.CO], 2018-2020.

%K nonn,more

%O 1,2

%A _N. J. A. Sloane_, Feb 13 2021