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A060125
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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.
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18
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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
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OFFSET
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0,3
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COMMENTS
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PermRank3Aux is a slight modification of rank2 algorithm presented in Myrvold-Ruskey article.
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LINKS
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MAPLE
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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))))
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CROSSREFS
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Cf. A056019 (compare the scatter plots).
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KEYWORD
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AUTHOR
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STATUS
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approved
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