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.

Showing 1-6 of 6 results.

A127296 Number of cycles in range [A014137(n-1)..A014138(n-1)] of permutation A127289/A127290.

Original entry on oeis.org

1, 1, 1, 1, 3, 4, 2, 5, 7, 8, 10, 18, 10
Offset: 0

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Author

Antti Karttunen, Jan 16 2007

Keywords

A127297 Maximum cycle size in range [A014137(n-1)..A014138(n-1)] of permutation A127289/A127290.

Original entry on oeis.org

1, 1, 2, 5, 10, 18, 86, 345, 866, 2639, 13341, 46236, 207882
Offset: 0

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Author

Antti Karttunen, Jan 16 2007

Keywords

Comments

Note that a(12)/A000108(12) = 207882/208012 = 0.9994..., i.e. one orbit visits over 99.9% percent of all the Cat(12) structures of size 12, leaving only 208012 - 207882 = 130 structures for other A127296(12)-1 = 9 cycles. Cf. A127298.

A127298 Least common multiple of all cycle sizes in range [A014137(n-1)..A014138(n-1)] of permutation A127289/A127290.

Original entry on oeis.org

1, 1, 2, 5, 30, 504, 1978, 714840, 500421564, 4855562127780, 1169461626163992, 112848995546998874467920, 7363180440
Offset: 0

Views

Author

Antti Karttunen, Jan 16 2007

Keywords

Comments

Note the non-monotone drop from a(11) to a(12). Cf. A127297.

A127289 Signature-permutation of a Catalan automorphism: composition of A127291 and A057164.

Original entry on oeis.org

0, 1, 3, 2, 6, 8, 7, 5, 4, 15, 20, 14, 19, 21, 18, 22, 16, 11, 13, 17, 12, 10, 9, 39, 53, 41, 55, 59, 40, 54, 38, 52, 57, 37, 51, 56, 58, 47, 60, 49, 62, 64, 48, 61, 43, 29, 34, 42, 28, 33, 35, 50, 63, 46, 32, 36, 44, 30, 25, 27, 45, 31, 26, 24, 23, 113, 155, 118, 160, 173
Offset: 0

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Author

Antti Karttunen, Jan 16 2007

Keywords

Comments

This is otherwise like A127291, but uses A127285 instead of A127287 as a "picker permutation" for the function "tau", which can be found in the entry A127291. A014486->parenthesization is given in A014486. This permutation contains some exceptionally large cycles, see A127297.

Links

Crossrefs

Inverse: A127290. a(n) = A127291(A057164(n)) = A057164(A127299(n)). The number of cycles, maximum cycle sizes and LCM's of all cycle sizes in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A127296, A127297 and A127298.

Programs

A127292 Signature-permutation of the inverse of Elizalde's and Deutsch's 2003 bijection for Dyck paths.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Jan 16 2007

Keywords

Comments

Note that this automorphism cannot be produced just by giving A127288 (the inverse of A127287) to function "tau" given in A127291. Instead, we have to use another algorithm given in A127300 and then conjugate it by A057164.

References

  • Emeric Deutsch and Sergi Elizalde, A simple and unusual bijection for Dyck paths and its consequences, Annals of Combinatorics, 7 (2003), no. 3, 281-297.

Links

Crossrefs

Inverse: A127291. a(n) = A057164(A127290(n)) = A057164(A127300(A057164(n))).

A127300 Signature-permutation of A057164-conjugate of the inverse of Elizalde's and Deutsch's 2003 bijection for Dyck paths.

Original entry on oeis.org

0, 1, 3, 2, 8, 4, 7, 6, 5, 22, 11, 17, 16, 12, 21, 9, 20, 19, 10, 18, 14, 13, 15, 64, 33, 48, 47, 34, 58, 23, 57, 56, 24, 49, 37, 35, 38, 63, 30, 45, 44, 31, 62, 28, 61, 60, 29, 46, 42, 32, 43, 59, 25, 54, 53, 26, 50, 39, 36, 40, 55, 51, 27, 52, 41, 196, 102, 145, 144, 103
Offset: 0

Views

Author

Antti Karttunen, Jan 16 2007

Keywords

Comments

Used to construct the inverse for A127291.

References

  • Emeric Deutsch and Sergi Elizalde, A simple and unusual bijection for Dyck paths and its consequences, Annals of Combinatorics, 7 (2003), no. 3, 281-297.

Links

Crossrefs

Inverse: A127299. a(n) = A057164(A127292(A057164(n))) = A127290(A057164(n)). Cf. A014486.
Showing 1-6 of 6 results.

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