A130374 Signature permutation of a Catalan automorphism: flip the positions of even- and odd-indexed elements at the top level of the list, leaving the last element in place if the length (A057515(n)) is odd.

0, 1, 2, 3, 4, 6, 5, 7, 8, 9, 10, 14, 16, 19, 11, 15, 12, 17, 18, 13, 20, 21, 22, 23, 25, 24, 26, 27, 37, 38, 42, 44, 47, 51, 53, 56, 60, 28, 29, 39, 43, 52, 30, 40, 31, 45, 46, 32, 48, 49, 50, 33, 41, 34, 54, 55, 35, 57, 58, 59, 36, 61, 62, 63, 64, 65, 66, 70, 72, 75, 67, 71

Offset: 0

Author

Antti Karttunen, Jun 05 2007

Keywords

• nonn
• look

Comments

This self-inverse automorphism permutes the top level of a list of even length (1 2 3 4 ... 2n-1 2n) as (2 1 4 3 ... 2n 2n-1), and when applied to a list of odd length (1 2 3 4 ... 2n-1 2n 2n+1), permutes it as (2 1 4 3 ... 2n 2n-1 2n+1).

Links

• Antti Karttunen, Table of n, a(n) for n = 0..2055
• Index entries for signature-permutations of Catalan automorphisms

Crossrefs

Cf. a(n) = A057508(A130373(A057508(n))) = A057164(A130373(A057164(n))) = A127285(A127288(n)) = A127287(A127286(n)). Also a(A085223(n)) = A130370(A122282(A130369(A085223(n)))) holds for all n>=0. The number of cycles and the number of fixed points in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A073193 and A073192.