A122286 -id:A122286 - cp's OEIS frontend

A131160 Signature permutation of a Catalan automorphism: row 21 of A122286.

0, 1, 3, 2, 8, 7, 6, 4, 5, 22, 21, 20, 18, 17, 19, 16, 14, 9, 10, 15, 11, 13, 12, 64, 63, 62, 59, 58, 61, 57, 55, 49, 50, 54, 48, 45, 46, 60, 56, 53, 47, 44, 51, 42, 37, 23, 24, 38, 25, 27, 26, 52, 43, 39, 28, 29, 41, 33, 36, 35, 40, 30, 34, 32, 31, 196, 195, 194, 190, 189

Offset: 0

Antti Karttunen, Jun 20 2007

nonn

Derived from automorphism *A130360 with recursion scheme SPINE.

Inverse: A131159.

A131162 Signature permutation of a Catalan automorphism: row 20 of A122286.

Original entry on oeis.org

0, 1, 3, 2, 8, 7, 4, 6, 5, 22, 21, 18, 20, 17, 10, 11, 14, 16, 19, 9, 15, 13, 12, 64, 63, 59, 62, 58, 50, 49, 55, 57, 61, 48, 54, 45, 46, 26, 27, 33, 29, 30, 38, 39, 42, 44, 47, 51, 53, 56, 60, 23, 28, 37, 43, 52, 24, 41, 36, 35, 25, 40, 32, 34, 31, 196, 195, 190, 194, 189

Offset: 0

Antti Karttunen, Jun 20 2007

nonn

Derived from automorphism *A130362 with recursion scheme SPINE.

Inverse: A131161.

A131164 Signature permutation of a Catalan automorphism: row 13 of A122286.

Original entry on oeis.org

0, 1, 3, 2, 8, 6, 7, 5, 4, 22, 19, 21, 15, 14, 20, 16, 17, 13, 11, 18, 12, 10, 9, 64, 60, 63, 52, 51, 62, 56, 58, 41, 39, 59, 40, 38, 37, 61, 53, 57, 43, 42, 54, 44, 45, 36, 33, 46, 35, 29, 28, 55, 47, 48, 34, 30, 49, 31, 27, 25, 50, 32, 26, 24, 23, 196, 191, 195, 178, 177

Offset: 0

Antti Karttunen, Jun 20 2007

nonn

Derived from automorphism *A130364 with recursion scheme SPINE.

Inverse: A131163.

A131166 Signature permutation of a Catalan automorphism: row 14 of A122286.

Original entry on oeis.org

0, 1, 3, 2, 6, 7, 8, 5, 4, 16, 15, 14, 17, 18, 19, 20, 21, 11, 12, 22, 13, 10, 9, 43, 44, 47, 39, 40, 42, 41, 38, 45, 46, 37, 48, 49, 50, 53, 52, 51, 54, 55, 56, 57, 58, 30, 29, 59, 28, 31, 32, 60, 61, 62, 33, 34, 63, 35, 25, 26, 64, 36, 27, 24, 23, 127, 123, 124, 128, 131

Offset: 0

Antti Karttunen, Jun 20 2007

nonn

Derived from automorphism *A130366 with recursion scheme SPINE.

Inverse: A131165.

A131168 Signature permutation of a Catalan automorphism: row 16 of A122286.

Original entry on oeis.org

0, 1, 3, 2, 6, 8, 7, 5, 4, 19, 14, 15, 21, 22, 16, 20, 17, 11, 13, 18, 12, 10, 9, 51, 60, 56, 38, 37, 52, 40, 39, 58, 59, 41, 62, 63, 64, 53, 42, 43, 57, 61, 44, 54, 45, 33, 28, 46, 29, 35, 36, 47, 55, 48, 30, 34, 49, 31, 25, 27, 50, 32, 26, 24, 23, 177, 149, 150, 186, 191

Offset: 0

Antti Karttunen, Jun 20 2007

nonn

Derived from automorphism *A130368 with recursion scheme SPINE.

Inverse: A131167.

A131170 Signature permutation of a Catalan automorphism: row 8 of A122286.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 7, 6, 8, 9, 10, 11, 12, 13, 17, 18, 16, 14, 15, 20, 19, 21, 22, 23, 24, 26, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 45, 46, 49, 48, 50, 44, 47, 42, 37, 38, 43, 40, 39, 41, 54, 55, 53, 51, 52, 57, 56, 58, 59, 61, 60, 62, 63, 64, 65, 66, 67, 68, 69, 73, 74

Offset: 0

Antti Karttunen, Jun 20 2007

nonn

Derived from automorphism *A082340 with recursion scheme SPINE.

Inverse: A131169.

A131172 Signature permutation of a Catalan automorphism: row 17 of A122286.

Original entry on oeis.org

0, 1, 3, 2, 8, 7, 5, 4, 6, 22, 21, 17, 18, 20, 12, 13, 10, 9, 11, 15, 14, 16, 19, 64, 63, 58, 59, 62, 46, 45, 48, 49, 50, 54, 55, 57, 61, 34, 32, 36, 35, 31, 27, 26, 24, 23, 25, 29, 28, 30, 33, 40, 41, 38, 37, 39, 43, 42, 44, 47, 52, 51, 53, 56, 60, 196, 195, 189, 190, 194

Offset: 0

Antti Karttunen, Jun 20 2007

nonn

Derived from automorphism *A074686 with recursion scheme SPINE.

Inverse: A131171.

A089840 Signature permutations of non-recursive Catalan automorphisms (i.e., bijections of finite plane binary trees, with no unlimited recursion down to indefinite distances from the root), sorted according to the minimum number of opening nodes needed in their defining clauses.

Original entry on oeis.org

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, 1, 0, 8, 4, 5, 4, 5, 3, 2, 1, 0, 9, 5, 7, 6, 6, 6, 3, 2, 1, 0, 10, 17, 8, 7, 4, 5, 6, 3, 2, 1, 0, 11, 18, 9, 8, 7, 4, 4, 4, 3, 2, 1, 0, 12, 20, 10, 12, 8, 7, 5, 5, 4, 3, 2, 1, 0, 13, 21, 14, 13, 12, 8, 7, 6

Offset: 0

Antti Karttunen, Dec 05 2003; last revised Jan 06 2009

Each row is a permutation of natural numbers and occurs only once. The table is closed with regards to the composition of its rows (see A089839) and it contains the inverse of each (their positions are shown in A089843). The permutations in table form an enumerable subgroup of the group of all size-preserving "Catalan bijections" (bijections among finite unlabeled rooted plane binary trees). The order of each element is shown at A089842.

A. Karttunen, paper in preparation, draft available by e-mail.

A. Karttunen, C-program for computing the terms of this table. Defines also the order of rows.
A. Karttunen, Prolog-program which illustrates the construction of each row

The first 22 rows of this table: row 0 (identity permutation): A001477, 1: A069770, 2: A072796, 3: A089850, 4: A089851, 5: A089852, 6: A089853, 7: A089854, 8: A072797, 9: A089855, 10: A089856, 11: A089857, 12: A074679, 13: A089858, 14: A073269, 15: A089859, 16: A089860, 17: A074680, 18: A089861, 19: A073270, 20: A089862, 21: A089863.
Other rows: row 83: A154125, row 169: A129611, row 183: A154126, row 251: A129612, row 253: A123503, row 258: A123499, row 264: A123500, row 3608: A129607, row 3613: A129605, row 3617: A129606, row 3655: A154121, row 3656: A154123,row 3702: A082354, row 3747: A154122, row 3748: A154124, row 3886: A082353, row 4069: A082351, row 4207: A089865, row 4253: A082352, row 4299: A089866, row 65167: A129609, row 65352: A129610, row 65518: A123495, row 65796: A123496, row 79361: A123492, row 1653002: A123695, row 1653063: A123696, row 1654023: A073281, row 1654249: A123498, row 1654694: A089864, row 1654720: A129604,row 1655089: A123497, row 1783367: A123713, row 1786785: A123714.
Tables A122200, A122201, A122202, A122203, A122204, A122283, A122284, A122285, A122286, A122287, A122288, A122289, A122290, A130400-A130403 give various "recursive derivations" of these non-recursive automorphisms. See also A089831, A073200.
Index sequences to this table, giving various subgroups or other important constructions: A153826, A153827, A153829, A153830, A123694, A153834, A153832, A153833.

A122285 Signature permutations of ENIPS-transformations of Catalan automorphisms in table A122203.

Original entry on oeis.org

0, 1, 0, 2, 1, 0, 3, 3, 1, 0, 4, 2, 2, 1, 0, 5, 8, 3, 2, 1, 0, 6, 7, 4, 3, 2, 1, 0, 7, 6, 6, 5, 3, 2, 1, 0, 8, 5, 5, 4, 5, 3, 2, 1, 0, 9, 4, 7, 6, 6, 6, 3, 2, 1, 0, 10, 22, 8, 7, 4, 5, 6, 3, 2, 1, 0, 11, 21, 9, 8, 7, 4, 4, 4, 3, 2, 1, 0, 12, 20, 14, 13, 8, 7, 5, 5, 4, 3, 2, 1, 0, 13, 18, 11, 12, 13

Offset: 0

Antti Karttunen, Sep 01 2006, Jun 20 2007

Row n is the signature permutation of the Catalan automorphism which is obtained from the n-th automorphism in the table A122203 with the recursion scheme "ENIPS", or equivalently row n is obtained as ENIPS(SPINE(n-th row of A089840)). See A122203 and A122204 for the description of SPINE and ENIPS. Each row occurs only once in this table. Inverses of these permutations can be found in table A122286. This table contains also all the rows of A122204 and A089840.

A. Karttunen, paper in preparation, draft available by e-mail.

Index entries for signature-permutations of Catalan automorphisms

The first 22 rows of this table: row 0 (identity permutation): A001477, 1: A082348, 2: A057508, 3: A131141, 4: A131143, 5: A131145, 6: A131147, 7: A131173, 8: A131169, 9: A131149, 10: A131151, 11: A131153, 12: A131171, 13: A131155, 14: A131157, 15: A131159, 16: A131161, 17: A057503, 18: A131163, 19: A131165, 20: A131167, 21: A069768. Other rows: row 251: A130360, 3608: A130339, 3613: A057510, 65352: A074686.

See also tables A089840, A122200, A122201-A122204, A122283-A122284, A122286-A122288, A122289-A122290, A130400-A130403. As a sequence differs from A122286 for the first time at n=92, where a(n)=18, while A122286(n)=17.

A122288 Signature permutations of KROF-transformations of Catalan automorphisms in table A122203.

Original entry on oeis.org

0, 1, 0, 2, 1, 0, 3, 3, 1, 0, 4, 2, 2, 1, 0, 5, 8, 3, 2, 1, 0, 6, 7, 4, 3, 2, 1, 0, 7, 6, 6, 5, 3, 2, 1, 0, 8, 4, 5, 4, 5, 3, 2, 1, 0, 9, 5, 7, 6, 6, 6, 3, 2, 1, 0, 10, 22, 8, 7, 4, 5, 6, 3, 2, 1, 0, 11, 21, 9, 8, 7, 4, 4, 4, 3, 2, 1, 0, 12, 20, 14, 13, 8, 7, 5, 5, 4, 3, 2, 1, 0, 13, 17, 11, 12, 13

Offset: 0

Antti Karttunen, Sep 01 2006, Jun 20 2007

Row n is the signature permutation of the Catalan automorphism which is obtained from the n-th automorphism in the table A122203 with the recursion scheme "KROF", or equivalently row n is obtained as KROF(SPINE(n-th row of A089840)). See A122202 and A122203 for the description of KROF and SPINE. Moreover, each row of A122288 can be obtained as the "NEPEED" transform of the corresponding row in A122285. (See A122284 for the description of NEPEED). Each row occurs only once in this table. Inverses of these permutations can be found in table A122287. This table contains also all the rows of A122202 and A089840.

A. Karttunen, paper in preparation, draft available by e-mail.

Index entries for signature-permutations of Catalan automorphisms

The first 22 rows of this table: row 0 (identity permutation): A001477, 1: A069768, 2: A057164, 3: A130981, 4: A130983, 5: A130982, 6: A130984, 7: A130985, 8: A130987, 9: A130989, 10: A130991, 11: A130993, 12: A131009, 13: A130995, 14: A130997, 15: A130999, 16: A131001, 17: A057505, 18: A131003, 19: A131005, 20: A131007, 21: A057163. Other rows: 251: A122354, 3613: A057512, 65352: A074682.

cp's OEIS Frontend

A131160 Signature permutation of a Catalan automorphism: row 21 of A122286.

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A131162 Signature permutation of a Catalan automorphism: row 20 of A122286.

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A131164 Signature permutation of a Catalan automorphism: row 13 of A122286.

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A131166 Signature permutation of a Catalan automorphism: row 14 of A122286.

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A131168 Signature permutation of a Catalan automorphism: row 16 of A122286.

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A131170 Signature permutation of a Catalan automorphism: row 8 of A122286.

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A131172 Signature permutation of a Catalan automorphism: row 17 of A122286.

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A089840 Signature permutations of non-recursive Catalan automorphisms (i.e., bijections of finite plane binary trees, with no unlimited recursion down to indefinite distances from the root), sorted according to the minimum number of opening nodes needed in their defining clauses.

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A122285 Signature permutations of ENIPS-transformations of Catalan automorphisms in table A122203.

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A122288 Signature permutations of KROF-transformations of Catalan automorphisms in table A122203.

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