A123714 Signature permutation of a nonrecursive Catalan automorphism: row 1786785 of table A089840.

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

Offset: 0

Author

Antti Karttunen, Oct 11 2006

Keywords

• nonn

Comments

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

.............................B...C............F...B......

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

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

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

.................................x...E............x...D..

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

..A...B.........C...A..............x...F............x...E

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

....x...C...-->...x...B..........()..x............()..x..

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

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

This is the last multiclause automorphism of total seven opened conses in the table A089840. The next nonrecursive automorphism, A089840[1786786], which consists of a single seven-node clause, swaps the first two toplevel elements (of a general plane tree, like *A072796 does), but only if A057515(n) > 6 and in other cases keeps the tree intact.

Links

• A. Karttunen, Table of n, a(n) for n = 0..6917
• 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: A123713. Row 1786785 of A089840. Differs from A089857 for the first time at n=102, where a(n)=106, while A089857(n)=102.