A319253 Number of doubly sorted permutations of [2n].

1, 3, 31, 1186

Offset: 1

Author

Colin Defant, Sep 15 2018

Keywords

• nonn
• more

Comments

A permutation pi is called doubly sorted if |s^{-1}(pi)| = 2, where s is West's stack-sorting map. There are no doubly sorted permutations of odd length.

Examples

			The a(2) = 3 doubly sorted permutations of [4] are 2314, 1324, and 3124. Specifically, letting s denote West's stack-sorting map, we have s^{-1}(2314) = {2341, 3241}, s^{-1}(1324) = {1342, 3142}, and s^{-1}(3124) = {3412, 3421}.
		

Links

• C. Defant, M. Engen, and J. A. Miller, Stack-sorting, set partitions, and Lassalle's sequence, arXiv:1809.01340 [math.CO], 2018.

Crossrefs

Cf. A180874, A317551.