A249165 Number of cds-sortable permutations in S_n. That is, number of permutations for which application of some sequence of context directed swaps ("cds" operations) terminates in the identity.
1, 1, 4, 13, 72, 390, 2880, 21672, 201600, 1935360, 21772800, 253756800, 3353011200, 45924278400
Offset: 1
Examples
a(3) = 4 because there are 4 cds-sortable permutations of {1,2,3}. These are, in one-line notation, 123, 132, 213, and 321.
Links
- K. L. M. Adamyk, E. Holmes, G. R. Mayfield, D. J. Moritz, M. Scheepers, B. E. Tenner, and H. C. Wauck, Sorting permutations: games, genomes, and cycles, arXiv:1410.2353 [math.CO], 2014.
- C. A. Brown, C. S. Carrillo Vazquez, R. Goswami, S. Heil, M. Scheepers, The Sortability of Graphs and Matrices under Context Directed Swaps, arXiv:1904.03287 [math.CO], 2019.
Extensions
a(11)-a(14) from Paul Plummer, Jan 18 2015