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.

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A125987 Signature-permutation of the square of Vaillé's 1997 bijection on Dyck paths.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 7, 5, 8, 9, 14, 16, 11, 15, 17, 20, 10, 12, 19, 21, 18, 13, 22, 23, 37, 42, 28, 39, 44, 43, 25, 30, 38, 40, 53, 29, 52, 45, 54, 57, 48, 55, 24, 51, 31, 26, 34, 47, 33, 56, 41, 58, 62, 46, 49, 61, 27, 35, 32, 60, 63, 59, 50, 36, 64, 65, 107, 121, 79, 112
Offset: 0

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Author

Antti Karttunen, Jan 02 2007

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Inverse: A125988. a(n) = A125985(A125985(n)). The number of cycles, 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 A126294, A126295, A126296 and A126297. The fixed points are given by A126298/A126299.

A126295 Number of fixed points in range [A014137(n-1)..A014138(n-1)] of permutation A125987/A125988.

Original entry on oeis.org

1, 1, 2, 2, 2, 3, 4, 5, 4, 4, 4, 4, 4, 7, 8, 7, 6, 10
Offset: 0

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Author

Antti Karttunen, Jan 02 2007

Keywords

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Fixed points themselves are given in A126298/A126299.

A126299 Factorial codes for the fixed points of the square of Vaillé's 1997 bijection on Dyck paths.

Original entry on oeis.org

0, 1, 11, 21, 111, 321, 1111, 4321, 11111, 23211, 54321, 111111, 122211, 324321, 654321, 1111111, 1222121, 2432211, 3244321, 7654321, 11111111, 22121321, 34443211, 87654321, 111111111, 122322121, 325543321, 987654321, 1111111111
Offset: 0

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Author

Antti Karttunen, Jan 02 2007

Keywords

Comments

From n=31 the terms cannot anymore be presented unambiguously with decimal numbers, as A126298(31)=23713, A071156(23713)=39916799 and A007623(39916799) would result the factorial expansion "T987654321", where T stands for digit "ten".

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Crossrefs

Cf. A071158, A126298.
Superset of A126301. Number of terms of length n is given by A126295(n).

Formula

a(n) = A071158(A126298(n)).

A126300 Fixed points of the permutation A125985/A125986.

Original entry on oeis.org

0, 1, 47, 443, 653479, 10269977
Offset: 0

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Author

Antti Karttunen, Jan 02 2007

Keywords

Comments

Those i, for which A125985(i)=i. A126301 shows the same fixed points using factorial code as employed in Vaillé's paper.

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Crossrefs

Subset of A126298. Cf. A126295. A126311(n) = A071156(a(n)).
Showing 1-4 of 4 results.

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

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