A123695 Signature permutation of a nonrecursive Catalan automorphism: row 1653002 of table A089840.

0, 1, 3, 2, 6, 7, 8, 5, 4, 14, 15, 16, 17, 18, 19, 20, 21, 11, 12, 22, 13, 9, 10, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 28, 29, 59, 30, 31, 32, 60, 61, 62, 33, 34, 63, 35, 23, 24, 64, 36, 25, 26, 27, 107, 108, 109, 110, 111

Offset: 0

Author

Antti Karttunen, Oct 11 2006

Keywords

• nonn

Comments

It is possible to recursively construct more of these kinds of nonrecursive automorphisms, which by default (if A057515(n) > 1) work as *A074679 and otherwise apply the previous automorphism of this construction process (here *A074679 itself) to the left subtree of a binary tree, before the whole tree is swapped with *A069770. Do the associated cycle-count sequences converge to anything interesting?

This automorphism is illustrated below, where letters A, B and C refer to arbitrary subtrees located on those nodes and () stands for an implied terminal node.

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

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

..B...C.....A...B........A...x............x...C...A..()...............()..A

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

A...x....-->..x...C........x..()...-->..()..x.......x..()....-->....()..x..

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

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

Links

• A. Karttunen, Prolog-program which illustrates the construction of this and other similar nonrecursive Catalan automorphisms.
• Index entries for signature-permutations of Catalan automorphisms

Crossrefs

Inverse: A123696. Row 1653002 of A089840. Variant of A074679.