A060125 - OEIS

A060125

Self-inverse infinite permutation which shows the position of the inverse of each finite permutation in A060117 (or A060118) in the same sequence; or equally, the cross-indexing between A060117 and A060118.

0, 1, 2, 5, 4, 3, 6, 7, 14, 23, 22, 15, 12, 19, 8, 11, 16, 21, 18, 13, 20, 17, 10, 9, 24, 25, 26, 29, 28, 27, 54, 55, 86, 119, 118, 87, 84, 115, 56, 59, 88, 117, 114, 85, 116, 89, 58, 57, 48, 49, 74, 101, 100, 75, 30, 31, 38, 47, 46, 39, 60, 67, 80, 107, 112, 93, 66, 61, 92

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

PermRank3Aux is a slight modification of rank2 algorithm presented in Myrvold-Ruskey article.

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..5040

W. Myrvold and F. Ruskey, Ranking and Unranking Permutations in Linear Time, Inform. Process. Lett. 79 (2001), no. 6, 281-284.

Index entries for sequences related to factorial base representation

Index entries for sequences that are permutations of the natural numbers

MAPLE

with(group); permul := (a, b) -> mulperms(b, a); swap := (p, i, j) -> convert(permul(convert(p, 'disjcyc'), [[i, j]]), 'permlist', nops(p));

PermRank3Aux := proc(n, p, q) if(1 = n) then RETURN(0); else RETURN((n-p[n])*((n-1)!) + PermRank3Aux(n-1, swap(p, n, q[n]), swap(q, n, p[n]))); fi; end;

PermRank3R := p -> PermRank3Aux(nops(p), p, convert(invperm(convert(p, 'disjcyc')), 'permlist', nops(p)));

PermRank3L := p -> PermRank3Aux(nops(p), convert(invperm(convert(p, 'disjcyc')), 'permlist', nops(p)), p);

# a(n) = PermRank3L(PermUnrank3R(n)) or PermRank3R(PermUnrank3L(n)) or PermRank3L(convert(invperm(convert(PermUnrank3L(j), 'disjcyc')), 'permlist', nops(PermUnrank3L(j))))

CROSSREFS

Cf. A060117, A060118, A060126, A060127, A275957, A275958.

Cf. A261220 (fixed points).

Cf. A056019 (compare the scatter plots).

Sequence in context: A265362 A264989 A328625 * A265361 A328626 A265357

Adjacent sequences: A060122 A060123 A060124 * A060126 A060127 A060128

KEYWORD

nonn,base,look

AUTHOR

Antti Karttunen, Mar 02 2001

STATUS

approved