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Search: id:A064640
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| A064640 |
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Positions of non-crossing fixed-point-free involutions (encoded by A014486) in A055089, sorted to ascending order. |
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7
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| 0, 1, 7, 23, 127, 143, 415, 659, 719, 5167, 5183, 5455, 5699, 5759, 16687, 16703, 26815, 28495, 36899, 36959, 38579, 40031, 40319, 368047, 368063, 368335, 368579, 368639, 379567, 379583, 389695, 391375, 399779, 399839, 401459, 402911, 403199
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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These permutations belong to the interpretation (kk) of the exercise 19 in the sixth chapter "Exercises on Catalan and Related Numbers" of Enumerative Combinatorics, Vol. 2, 1999 by R. P. Stanley, Wadsworth, Vol. 1, 1986: Fixed-point-free involutions w of [2n] such that if i < j < k < l and w(i) = k, then w(j) <> l.
From which follows that when they are subjected to the same automorphism as used in A061417 and A064636 one gets A002995.
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LINKS
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R. P. Stanley, Exercises on Catalan and Related Numbers
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EXAMPLE
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The eight first such permutations (after the identity) are in positions 1, 7, 23, 127, 143, 415, 659, 719 of A055089: 21, 2143, 4321, 214365, 432165, 216543, 632541, 654321 which written as disjoint cycles are: (1 2), (1 2)(3 4), (1 4)(2 3), (1 2)(3 4)(5 6), (1 4)(2 3)(5 6), (1 2)(3 6)(4 5), (1 6)(2 3)(4 5), (1 6)(2 5)(3 4)
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MAPLE
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sort(A064638); or sort(A064639);
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CROSSREFS
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For the needed Maple procedures see A064638. Cf. also A064639, A060112.
Sequence in context: A096327 A053706 A137367 this_sequence A064639 A064638 A082021
Adjacent sequences: A064637 A064638 A064639 this_sequence A064641 A064642 A064643
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen Oct 02 2001
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