0,3

This automorphism either swaps (if A057515(n) > 1) the first two toplevel elements (of a general plane tree, like *A072796 does) and otherwise (if n > 1, A057515(n)=1) swaps the sides of the left hand side subtree of the S-expression (when viewed as a binary tree, like *A089854 does). This 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...C............A...B...........B...A

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

.A...x.....-->.....B...x................x..()....-->....x..()

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

...x....(A072796)....x....................x...(A089854)...x

(a . (b . c)) --> (b . (a . c)) / ((a . b) . ()) --> ((b . a) . ())

This is the first multiclause automorphism in table A089840 which cannot be represented as a composition of two smaller nonrecursive automorphisms, the property which is also shared by *A123499 and *A123500.

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

Index entries for signature-permutations of Catalan automorphisms

(Scheme function, destructive implementation of this automorphism acting on S-expressions:) (define (*A123503! s) (cond ((null? s) s) ((pair? (cdr s)) (*A072796! s)) (else (*A089854! s))) s)

Row 253 of A089840. Used to construct A123717 and A123718.

Sequence in context: A129258 A104650 A083179 this_sequence A123717 A123718 A121878

Adjacent sequences: A123500 A123501 A123502 this_sequence A123504 A123505 A123506

nonn

Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Oct 11 2006