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%I #7 Sep 24 2020 03:38:44
%S 1,1,1,2,3,4,7,11,16,26,42
%N Maximum number of preimages that a permutation of length n can have under the consecutive-123-avoiding stack-sorting map.
%H Colin Defant and Kai Zheng, <a href="https://arxiv.org/abs/2008.12297">Stack-sorting with consecutive-pattern-avoiding stacks</a>, arXiv:2008.12297 [math.CO], 2020.
%e The consecutive-123-avoiding stack-sorting map acts on permutations of length 3 by reversing every permutation except 321, which gets sent to 213. The permutation 213 has 2 preimages under this map (namely, 312 and 321), and every other permutation of length 3 has at most one preimage. Hence, a(3)=2.
%K nonn,more
%O 0,4
%A _Colin Defant_, Aug 29 2020