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A154123
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Signature permutation of a Catalan bijection: row 3656 of A089840.
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4
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0, 1, 2, 3, 5, 6, 4, 7, 8, 11, 12, 13, 16, 19, 15, 14, 9, 17, 18, 10, 20, 21, 22, 28, 29, 30, 31, 32, 33, 34, 35, 44, 47, 36, 53, 56, 60, 39, 40, 41, 42, 51, 43, 37, 23, 45, 46, 24, 48, 49, 50, 52, 38, 25, 54, 55, 26, 57, 58, 59, 27, 61, 62, 63, 64, 79, 80, 81, 82, 83, 84, 85
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| This bijection of binary trees is obtained in the following way. See also comments at A154122.
....C...D.......B...C
.....\./.........\./
..B...x....-->....x...D.................B..().........()..A..
...\./.............\./...................\./....-->....\./...
A...x...........A...x.................A...x.........B...x....
.\./.............\./...................\./...........\./.....
..x...............x.....................x.............x......
.............................................................
That is, we do (a . (b . (c . d))) -> (a . ((b . c) . d))
or (a . (b . ())) --> (b . (() . a)) if the former is not possible.
Note that the first clause corresponds to generator B of Thompson's groups F, T and V. See further comments at A154121.
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REFERENCES
| J. W. Cannon, W. J. Floyd and W. R. Parry, Introductory notes on Richard Thompson's groups, L'Enseignement Mathematique, Vol. 42 (1996), pp. 215--256.
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LINKS
| A. Karttunen, Table of n, a(n) for n = 0..2055
J. W. Cannon, W. J. Floyd and W. R. Parry, Notes on Richard Thompson's Groups F and T
Index entries for signature-permutations of Catalan automorphisms
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PROG
| (Destructive version of this automorphism in Scheme:) (define (*A154123! s) (if (and (pair? s) (pair? (cdr s)) (pair? (cddr s))) (*A074679! (cdr s)) (*A089851! s)) s)
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CROSSREFS
| Inverse: A154124. Cf. A154121.
Sequence in context: A094872 A201744 A152206 * A082353 A130343 A130381
Adjacent sequences: A154120 A154121 A154122 * A154124 A154125 A154126
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KEYWORD
| nonn
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AUTHOR
| Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Jan 06 2009
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