A212417
Size of the equivalence class of S_n containing the identity permutation under transformations of positionally adjacent elements of the form abc <--> acb <--> bac where a
1, 1, 1, 3, 7, 35, 135, 945, 5193, 46737
Offset: 0
Examples
From _Alois P. Heinz_, May 16 2012: (Start)
a(3) = 3: {123, 132, 213}.
a(4) = 7: {1234, 1243, 1324, 1423, 2134, 2143, 2314}. (End)
Links
- J. Cassaigne, M. Espie, D. Krob, J.-C. Novelli, F. Hivert, The Chinese Monoid, Int'l. J. Algebra and Comp. 11 (2001), 301-334.
- Z. Hamaker, E. Marberg, B. Pawlowski, Involution words II: braid relations and atomic structures, arXiv preprint arXiv:1601.02269 [math.CO], 2016. See Remark following Th. 6.18.
- S. Linton, J. Propp, T. Roby, and J. West, Equivalence Classes of Permutations under Various Relations Generated by Constrained Transpositions, arXiv:1111.3920 [math.CO], 2011, J. Int. Seq. 15 (2012) #12.9.1
Extensions
a(0)-a(2), a(9) from Alois P. Heinz, May 16 2012