A337495 Maximum number of preimages that a permutation of length n can have under the consecutive-123-avoiding stack-sorting map.
1, 1, 1, 2, 3, 4, 7, 11, 16, 26, 42
Offset: 0
Examples
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.
Links
- Colin Defant and Kai Zheng, Stack-sorting with consecutive-pattern-avoiding stacks, arXiv:2008.12297 [math.CO], 2020.