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%I #9 Jul 12 2012 00:39:49
%S 0,1,0,2,1,0,3,3,1,0,4,2,2,1,0,5,7,3,2,1,0,6,8,4,3,2,1,0,7,6,6,5,3,2,
%T 1,0,8,5,5,4,5,3,2,1,0,9,4,7,6,6,6,3,2,1,0,10,17,8,7,4,5,6,3,2,1,0,11,
%U 18,9,8,7,4,4,4,3,2,1,0,12,20,14,13,8,7,5,5,4,3,2,1,0,13,21,11,12,13
%N Signature permutations of FORK-transformations of Catalan automorphisms in table A122204.
%C Row n is the signature permutation of the Catalan automorphism which is obtained from the n-th automorphism in the table A122204 with the recursion scheme "FORK", or equivalently row n is obtained as FORK(ENIPS(n-th row of A089840)). See A122201 and A122204 for the description of FORK and ENIPS. Moreover, each row of A122287 can be obtained as the "DEEPEN" transform of the corresponding row in A122286. (See A122283 for the description of DEEPEN). Each row occurs only once in this table. Inverses of these permutations can be found in table A122288. This table contains also all the rows of A122201 and A089840.
%D A. Karttunen, paper in preparation, draft available by e-mail.
%H <a href="/index/Per#IntegerPermutationCatAuto">Index entries for signature-permutations of Catalan automorphisms</a>
%Y The first 22 rows of this table: row 0 (identity permutation): A001477, 1: A069767, 2: A057164, 3: A130981, 4: A130983, 5: A130982, 6: A130984, 7: A130986, 8: A130988, 9: A130994, 10: A130992, 11: A130990, 12: A057506, 13: A131004, 14: A131006, 15: A057163, 16: A131008, 17: A131010, 18: A130996, 19: A130998, 20: A131002, 21: A131000. Other rows: 169: A122353, 3617: A057511, 65167: A074681.
%Y See also tables A089840, A122200, A122201-A122204, A122283-A122284, A122285-A122288, A122289-A122290, A130400-A130403.
%K nonn,tabl
%O 0,4
%A _Antti Karttunen_, Sep 01 2006, Jun 20 2007
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