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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. 8
1, 1, 1, 3, 7, 35, 135, 945, 5193, 46737 (list; graph; refs; listen; history; text; internal format)
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: A179115 A299300 A047907 * 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

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Last modified March 22 17:25 EDT 2019. Contains 321422 sequences. (Running on oeis4.)