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<b<c.

1, 1, 1, 3, 7, 35, 135, 945, 5193, 46737

Offset

0,4

Links

Table of n, a(n) for n=0..9.

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

Example

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)

Crossrefs

Cf. A210667, A210668, A210669, A210671, A212417.

Sequence in context: A047907 A328420 A336012 * A145874 A147681 A055487

Adjacent sequences: A212414 A212415 A212416 * A212418 A212419 A212420

Keyword

nonn,more

Author

Tom Roby, May 15 2012

Extensions

a(0)-a(2), a(9) from Alois P. Heinz, May 16 2012

Status

approved