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

0,3

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

Table of n, a(n) for n=0..71.

A. Karttunen, Prolog-program which illustrates the construction of this and other similar nonrecursive Catalan automorphisms.

Index entries for signature-permutations of Catalan automorphisms

Prog

(Scheme function, destructive implementation of this automorphism acting on S-expressions:) (define (*A123492! s) (cond ((null? s) s) ((and (pair? (cdr s)) (pair? (cadr s))) (*A069770! s)) ((and (pair? (car s)) (pair? (caar s))) (*A069770! s))) s)

Crossrefs

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

Sequence in context: A338242 A353827 A353826 * A123493 A123715 A082313

Adjacent sequences: A123489 A123490 A123491 * A123493 A123494 A123495

Keyword

nonn

Author

Antti Karttunen, Oct 11 2006

Status

approved