A154122 Signature permutation of a Catalan bijection: row 3747 of A089840.

0, 1, 2, 3, 5, 4, 6, 7, 8, 12, 13, 9, 10, 11, 15, 14, 16, 17, 18, 19, 20, 21, 22, 31, 32, 34, 35, 36, 23, 24, 25, 26, 27, 28, 29, 30, 33, 40, 41, 37, 38, 39, 43, 42, 44, 45, 46, 47, 48, 49, 50, 52, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 87, 88, 90, 91, 92, 96, 97

Offset

0,3

Comments

This bijection of binary trees can be obtained by applying bijection *A074680 to the right hand side subtree and leaving the left hand side subtree intact. See also comments at A154121.

.B...C...............C...D

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

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

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

.A...x...........A...x.................A...x.........A...x....

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

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

..............................................................

That is, (a . ((b . c) . d)) -> (a . (b . (c . d)))

or (a . (() . c)) -> (a . (c . ())) if the former is not possible.

Links

A. Karttunen, Table of n, a(n) for n = 0..2055

Index entries for signature-permutations of Catalan automorphisms

Prog

(Destructive version of this automorphism in Scheme:) (define (*A154122! s) (if (pair? s) (*A074680! (cdr s))) s)

Crossrefs

Inverse: A154121. a(n) = A069770(A089866(A069770(n))). Cf. A154124.

Sequence in context: A216250 A154121 A130375 * A089850 A154450 A154449

Adjacent sequences: A154119 A154120 A154121 * A154123 A154124 A154125

Keyword

nonn

Author

Antti Karttunen, Jan 06 2009

Status

approved