A123492 An involution of nonnegative integers: signature permutation of a nonrecursive Catalan automorphism which swaps the sides of a binary tree if the left subtree of either the left or right hand side toplevel subtree is not empty and otherwise keeps the binary tree intact.

0, 1, 2, 3, 4, 8, 6, 7, 5, 9, 10, 20, 21, 22, 14, 19, 16, 17, 18, 15, 11, 12, 13, 23, 24, 25, 26, 27, 54, 55, 57, 58, 59, 61, 62, 63, 64, 37, 38, 53, 56, 60, 42, 51, 44, 45, 46, 47, 48, 49, 50, 43, 52, 39, 28, 29, 40, 30, 31, 32, 41, 33, 34, 35, 36, 65, 66, 67, 68, 69, 70, 71

Offset: 0

Author

Antti Karttunen, Oct 11 2006

Keywords

• nonn

Comments

This automorphism effects the following transformation on the unlabeled rooted plane binary trees (letters A, B, C and D refer to arbitrary subtrees located on those nodes.)

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

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

.......x...D.....x...D...........x...C.............x...C.

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

.....A...x...-->...x...A...........x...D...-->...D...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

Row 79361 of A089840. Used to construct A123493, A123494, A123715 and A123716. Cf. A069770.