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A060118
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A list of all finite permutations in "PermUnrank3L" ordering. (Inverses of the permutations of A060117).
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12
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1, 2, 1, 1, 3, 2, 2, 3, 1, 3, 2, 1, 3, 1, 2, 1, 2, 4, 3, 2, 1, 4, 3, 1, 3, 4, 2, 2, 3, 4, 1, 3, 2, 4, 1, 3, 1, 4, 2, 1, 4, 3, 2, 2, 4, 3, 1, 1, 4, 2, 3, 2, 4, 1, 3, 3, 4, 1, 2, 3, 4, 2, 1, 4, 2, 3, 1, 4, 1, 3, 2, 4, 3, 2, 1, 4, 3, 1, 2, 4, 2, 1, 3, 4, 1, 2, 3, 1, 2, 3, 5, 4, 2, 1, 3, 5, 4, 1, 3, 2, 5, 4, 2, 3, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| In contrast to PermUnrank3R (A060117), PermUnrank3L applies each successive transposition from the left, not from the right, thus producing the inverse (permutation) of what PermUnrank3R would produce.
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FORMULA
| [seq(op(PermUnrank3L(j)), j=0..)]; (Maple code given below)
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EXAMPLE
| In this table each row consists of A001563[n] permutations of (n+1) terms;
Append to each an infinite amount of fixed terms and we get a list of rearrangements of natural numbers, but with only a finite number of terms permuted:
1/2,3,4,5,6,7,8,9,...
2,1/3,4,5,6,7,8,9,...
1,3,2/4,5,6,7,8,9,...
2,3,1/4,5,6,7,8,9,...
3,2,1/4,5,6,7,8,9,...
3,1,2/4,5,6,7,8,9,...
1,2,4,3/5,6,7,8,9,...
2,1,4,3/5,6,7,8,9,...
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MAPLE
| with(group); permul := (a, b) -> mulperms(b, a); PermUnrank3L := proc(r) local n; n := nops(factorial_base(r)); convert(PermUnrank3Laux(n+1, r, []), 'permlist', 1+(((r+2) mod (r+1))*n)); end; PermUnrank3Laux := proc(n, r, p) local s; if(0 = r) then RETURN(p); else s := floor(r/((n-1)!)); RETURN(PermUnrank3Laux(n-1, r-(s*((n-1)!)), permul([[n, n-s]], p))); fi; end;
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CROSSREFS
| A060120 = Positions of these permutations in the "canonical list" A055089. Cf. also A060117.
Sequence in context: A120643 A111867 A133776 * A029308 A029259 A159266
Adjacent sequences: A060115 A060116 A060117 * A060119 A060120 A060121
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KEYWORD
| nonn
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AUTHOR
| Antti Karttunen Mar 02 2001
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