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

Author

Antti Karttunen, Jan 06 2009

Keywords

• nonn

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

Crossrefs

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