cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-20 of 32 results. Next

A130370 Signature permutation of a Catalan automorphism: inverse of *A130369.

Original entry on oeis.org

0, 1, 3, 2, 7, 8, 4, 5, 6, 17, 18, 20, 21, 22, 10, 9, 11, 12, 13, 14, 15, 16, 19, 45, 46, 48, 49, 50, 54, 55, 57, 58, 59, 61, 62, 63, 64, 26, 27, 23, 24, 25, 29, 28, 30, 31, 32, 33, 34, 35, 36, 38, 37, 39, 40, 41, 42, 43, 44, 47, 51, 52, 53, 56, 60, 129, 130, 132, 133, 134
Offset: 0

Views

Author

Antti Karttunen, Jun 05 2007

Keywords

Links

Crossrefs

Inverse: A130369. a(n) = A130371(A074686(n)) = A074686(A130375(n)). The number of cycles, number of fixed points, maximum cycle sizes and LCM's of all cycle sizes in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A130377, LEFT(A019590), A130378 and A130379.

A082351 Permutation of natural numbers induced by the Catalan bijection gma082351 acting on the parenthesizations encoded by A014486/A063171.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Apr 17 2003

Keywords

Links

Crossrefs

Inverse of A082352. a(n) = A057163(A082353(A057163(n))). Cf. also A074679-A074680, A082355-A082356, A082361-A082362.

A082352 Permutation of natural numbers induced by the Catalan bijection gma082352 acting on the parenthesizations encoded by A014486/A063171.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Apr 17 2003

Keywords

Links

Crossrefs

Inverse of A082351. a(n) = A057163(A082354(A057163(n))). Cf. also A074679-A074680, A082355-A082356, A082361-A082362.

A082335 Permutation of natural numbers induced by the Catalan bijection gma082335 acting on the parenthesizations encoded by A014486/A063171.

Original entry on oeis.org

0, 1, 3, 2, 6, 7, 8, 5, 4, 14, 15, 16, 17, 18, 19, 20, 21, 13, 12, 22, 11, 10, 9, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 36, 35, 59, 34, 32, 31, 60, 61, 62, 33, 30, 63, 29, 27, 26, 64, 28, 25, 24, 23, 107, 108, 109, 110, 111
Offset: 0

Views

Author

Antti Karttunen, Apr 17 2003

Keywords

Comments

This Catalan bijection rotates binary trees left, if possible, otherwise reflects them with the Catalan bijection A057163.

Links

Crossrefs

Inverse of A082336. Cf. also A074679-A074680, A082349-A082350.
Number of fixed-points: A019590. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).

A082336 Permutation of natural numbers induced by the Catalan bijection gma082336 acting on the parenthesizations encoded by A014486/A063171.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Apr 17 2003

Keywords

Comments

This Catalan bijection rotates binary trees right, if possible, otherwise reflects them with the Catalan bijection A057163.

Links

Crossrefs

Inverse of A082335. Cf. also A074679-A074680, A082349-A082350.
Number of fixed-points: A019590. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).

A082349 Permutation of natural numbers induced by the Catalan bijection gma082349 acting on the parenthesizations encoded by A014486/A063171.

Original entry on oeis.org

0, 1, 3, 2, 6, 7, 8, 5, 4, 14, 15, 16, 17, 18, 19, 20, 21, 12, 13, 22, 11, 10, 9, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 31, 32, 59, 34, 35, 36, 60, 61, 62, 30, 33, 63, 29, 26, 27, 64, 28, 25, 24, 23, 107, 108, 109, 110, 111
Offset: 0

Views

Author

Antti Karttunen, Apr 17 2003

Keywords

Comments

This Catalan bijection rotates binary trees left, if possible, otherwise applies Catalan bijection A069767.

Links

Crossrefs

Inverse of A082350. Cf. also A074679-A074680, A082335-A082336.
Number of cycles: A073193 (to be checked). Number of fixed-points: A019590. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).

A082350 Permutation of natural numbers induced by the Catalan bijection gma082350 acting on the parenthesizations encoded by A014486/A063171.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Apr 17 2003

Keywords

Comments

This Catalan bijection rotates binary trees right, if possible, otherwise applies Catalan bijection A069768.

Links

Crossrefs

Inverse of A082349. Cf. also A074679-A074680, A082335-A082336.
Number of cycles: A073193 (to be checked). Number of fixed-points: A019590. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right).

A089866 Permutation of natural numbers induced by Catalan Automorphism *A089866 acting on the parenthesizations/binary trees encoded by A014486/A063171.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Dec 20 2003

Keywords

Comments

This bijection of binary trees is obtained when we apply bijection *A074680 to the left subtree and keep the right subtree intact.
.A...B...............B...C
..\./.................\./
...x...C....-->....A...x.................()..B.........B...()....
....\./.............\./...................\./....-->....\./.....
.....x...D...........x...D.................x...C.........x...C..
......\./.............\./...................\./...........\./...
.......x...............x.....................x.............x....
................................................................
Compare to A154122.
See "Catalan bijections" OEIS-Wiki page for a detailed explanation how to obtain a given integer sequence from this definition.

Links

Crossrefs

Row 4299 of A089840. Inverse of A089865. a(n) = A069770(A154122(A069770(n))).
Number of cycles: A089844. Number of fixed-points: A005807 (prepended with two 1's). Max. cycle size: A089410. LCM of cycle sizes: A089845 (in each range limited by A014137 and A014138).

Extensions

Further comments and constructive version of Scheme-implementation added by Antti Karttunen, Jun 04 2011

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

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jan 06 2009

Keywords

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

Crossrefs

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

A123497 Signature permutation of a nonrecursive Catalan automorphism: row 1655089 of table A089840.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 7, 5, 8, 9, 10, 14, 16, 19, 17, 18, 12, 11, 13, 20, 15, 21, 22, 23, 24, 25, 26, 27, 37, 38, 42, 44, 47, 51, 53, 56, 60, 45, 46, 48, 49, 50, 31, 32, 30, 28, 29, 34, 33, 35, 36, 54, 55, 40, 39, 41, 57, 43, 58, 59, 61, 52, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71
Offset: 0

Views

Author

Antti Karttunen, Oct 11 2006

Keywords

Links

Crossrefs

Inverse: A123498. Row 1655089 of A089840. Used to construct automorphism *A123501. A074680(n) = A083927(a(A057123(n))).
Previous Showing 11-20 of 32 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.