A154126 Self-inverse signature permutation of a Catalan bijection: row 183 of A089840.

0, 1, 3, 2, 7, 8, 6, 4, 5, 17, 18, 20, 21, 22, 14, 15, 16, 9, 10, 19, 11, 12, 13, 45, 46, 48, 49, 50, 54, 55, 57, 58, 59, 61, 62, 63, 64, 37, 38, 39, 40, 41, 42, 43, 44, 23, 24, 47, 25, 26, 27, 51, 52, 53, 28, 29, 56, 30, 31, 32, 60, 33, 34, 35, 36, 129, 130, 132, 133, 134

Offset

0,3

Comments

This bijection of binary trees swaps the left and right subtree of a binary tree, but ONLY if either of them is empty. If both the left and right hand side tree is nonempty, fixes the tree.

.A...B.C...D.......A...B.C...D.....

..\./...\./.........\./...\./........................

...x.....x...--->....x.....x.......A...B.......B...A.

....\.../.............\.../.........\./..--->...\./..

......x.................x............x...........x...

..............................(where either A or B is (), a leaf)

This automorphism demonstrates that not every clause in clause-representations of A089840 is equal to some (minimally represented) element of Thompson's group V.

Links

A. Karttunen, Table of n, a(n) for n = 0..2055

J. W. Cannon, W. J. Floyd, and W. R. Parry, Introductory notes on Richard Thompson's groups, L'Enseignement Mathématique, Vol. 42 (1996), pp. 215-256.

Index entries for signature-permutations of Catalan automorphisms

Prog

(Destructive version of this automorphism in Scheme:) (define (*A154126! s) (if (and (pair? s) (or (not (pair? (car s))) (not (pair? (cdr s))))) (*A069770! s)) s)

Crossrefs

Inverse: A154126. a(n) = A069770(A154125(n)) = A154125(A069770(n)).

Sequence in context: A125984 A130959 A130928 * A069770 A129612 A154455

Adjacent sequences: A154123 A154124 A154125 * A154127 A154128 A154129

Keyword

nonn

Author

Antti Karttunen, Jan 06 2009

Status

approved