Permutation of natural numbers induced by the gatomorphism Catalan bijection gma082335 acting on the parenthesizations encoded by A014486/A063171.

This gatomorphism Catalan bijection rotates binary trees left, if possible, otherwise reflects them with the gatomorphism Catalan bijection A057163.

_Antti Karttunen (Firstname.Surname(AT)iki.fi), _, Apr 17 2003

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

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

nonn,new

nonn

A. Karttunen, <A HREFa href="http://www.iki.fi/~kartturi/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</Aa> (with the complete Scheme source)

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

nonn,new

nonn

Number of fixpointsfixed-points: A019590. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).

nonn,new

nonn

Cf. Number of fixpoints: A019590. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).

nonn,new

nonn

Permutation of natural numbers induced by the gatomorphism gma082335 acting on the parenthesizations encoded by A014486/A063171.

0, 1, 3, 2, 6, 7, 8, 5, 4, 14, 15, 16, 17, 18, 19, 20, 21, 13, 12, 22, 11, 10, 9, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 36, 35, 59, 34, 32, 31, 60, 61, 62, 33, 30, 63, 29, 27, 26, 64, 28, 25, 24, 23, 107, 108, 109, 110, 111

0,3

This gatomorphism rotates binary trees left, if possible, otherwise reflects them with the gatomorphism A057163.

A. Karttunen, <A HREF="http://www.iki.fi/~kartturi/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</A> (with the complete Scheme source)

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

(Scheme functions implementing this automorphism on list-structures:)

(define (gma082335! s) (cond ((pair? s) (cond ((pair? (cdr s)) (robl! s)) (else (gma057163! s))))) s)

(define (robl! s) (let ((ex-car (car s))) (set-car! s (cddr s)) (set-cdr! (cdr s) ex-car) (swap! (cdr s)) (swap! s) s))

(define (swap! s) (let ((ex-car (car s))) (set-car! s (cdr s)) (set-cdr! s ex-car) s))

Inverse of A082336. Cf. also A074679-A074680, A082349-A082350.

Cf. Number of fixpoints: A019590. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).

nonn

Antti Karttunen (Firstname.Surname(AT)iki.fi), Apr 17 2003

approved