

A122200


Signature permutations of RIBStransformations of nonrecursive Catalan automorphisms in table A089840.


20



0, 1, 0, 2, 1, 0, 3, 2, 1, 0, 4, 3, 2, 1, 0, 5, 4, 3, 2, 1, 0, 6, 5, 4, 3, 2, 1, 0, 7, 6, 5, 4, 3, 2, 1, 0, 8, 8, 6, 5, 4, 3, 2, 1, 0, 9, 7, 7, 6, 5, 4, 3, 2, 1, 0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 13, 13, 11, 10, 9, 8
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OFFSET

0,4


COMMENTS

Row n is the signature permutation of the Catalan automorphism which is obtained from the nth nonrecursive automorphism in the table A089840 with the recursion scheme "RIBS".
In this recursion scheme the given automorphism is applied to all (toplevel) subtrees of the Catalan structure, when it is interpreted as a general tree. Permutations in this table form a countable group, which is isomorphic with the group in A089840. (The RIBS transformation gives the group isomorphism.)
Furthermore, row n of this table is also found as the row A123694(n) in tables A122203 and A122204. If the count of fixed points of the automorphism A089840[n] is given by sequence f, then the count of fixed points of the automorphism A089840[A123694(n)] is given by CONV(f,A000108) (where CONV stands for convolution) and the count of fixed points of the automorphism A122200[n] by INVERT(RIGHT(f)).
The associated Schemeprocedures RIBS and !RIBS can be used to obtain such a transformed automorphism from any constructively or destructively implemented automorphism.
Comment from Antti Karttunen, May 11 2008: This sequence agrees with A025581 in its initial terms, but then diverges from it.


REFERENCES

A. Karttunen, paper in preparation, draft available by email.


LINKS

Table of n, a(n) for n=0..96.
Index entries for signaturepermutations of Catalan automorphisms


PROG

(Scheme) (define (RIBS foo) (lambda (s) (map foo s)))
(define (!RIBS foo!) (letrec ((bar! (lambda (s) (cond ((pair? s) (foo! (car s)) (bar! (cdr s)))) s))) bar!))


CROSSREFS

Row 0 (identity permutation): A001477, row 1: A122282. See also tables A089840, A122201A122204, A122283A122284, A122285A122288, A122289A122290.
Sequence in context: A025651 A330238 A025670 * A025646 A025661 A025671
Adjacent sequences: A122197 A122198 A122199 * A122201 A122202 A122203


KEYWORD

nonn,tabl


AUTHOR

Antti Karttunen, Sep 01 2006


STATUS

approved



