login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A122200 Signature permutations of RIBS-transformations of non-recursive 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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Row n is the signature permutation of the Catalan automorphism which is obtained from the n-th 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 Scheme-procedures 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 e-mail.

LINKS

Table of n, a(n) for n=0..96.

Index entries for signature-permutations 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, A122201-A122204, A122283-A122284, A122285-A122288, A122289-A122290.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 09:33 EST 2019. Contains 329843 sequences. (Running on oeis4.)