_Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), _, Jun 05 2007

<a href="/Sindx_index/Per.html#IntegerPermutationCatAuto">Index entries for signature-permutations of Catalan automorphisms</a>

A. Karttunen, <a href="/A130371/b130371.txt">Table of n, a(n) for n = 0..2055</a>

<a href="/Sindx_Per.html#IntegerPermutationCatAuto">Index entries for signature-permutations of Catalan automorphisms</a>

nonn,new

nonn

A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/b130371.txt">Table of n, a(n) for n = 0..2055</a>

<A HREFa href="http://www.research.att.com/~njas/sequences/Sindx_Per.html#IntegerPermutationCatAuto">Index entries for signature-permutations of Catalan automorphisms</Aa>

nonn,new

nonn

Signature permutation of a Catalan automorphism: apply *A074685 to the last subtree, if the root degree (A057515(n)) is odd.

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

0,3

A. Karttunen, <a href="http://www.research.att.com/~njas/sequences/b130371.txt">Table of n, a(n) for n = 0..2055</a>

<A HREF="http://www.research.att.com/~njas/sequences/Sindx_Per.html#IntegerPermutationCatAuto">Index entries for signature-permutations of Catalan automorphisms</A>

(Destructive Scheme implementation of this automorphism, which acts on S-expressions, i.e. list-structures:)

(define (*A130371! s) (if (odd? (length s)) (*A074685! (car (last-pair s)))) s)

Inverse: A130372. a(n) = A130370(A074685(n)) = A074686(A130375(A074685(n))) = A130370(A130375(A130369(n))).

nonn

Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Jun 05 2007

approved