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Search: id:A060117
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| A060117 |
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A list of all finite permutations in "PermUnrank3R" ordering. (Inverses of the permutations of A060118). |
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21
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| 1, 2, 1, 1, 3, 2, 3, 1, 2, 3, 2, 1, 2, 3, 1, 1, 2, 4, 3, 2, 1, 4, 3, 1, 4, 2, 3, 4, 1, 2, 3, 4, 2, 1, 3, 2, 4, 1, 3, 1, 4, 3, 2, 4, 1, 3, 2, 1, 3, 4, 2, 3, 1, 4, 2, 3, 4, 1, 2, 4, 3, 1, 2, 4, 2, 3, 1, 2, 4, 3, 1, 4, 3, 2, 1, 3, 4, 2, 1, 3, 2, 4, 1, 2, 3, 4, 1, 1, 2, 3, 5, 4, 2, 1, 3, 5, 4, 1, 3, 2, 5, 4, 3, 1, 2
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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PermUnrank3R and PermUnrank3L are slight modifications of unrank2 algorithm presented in Myrvold-Ruskey article.
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LINKS
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W. Myrvold and F. Ruskey, Ranking and Unranking Permutations in Linear Time, Inform. Process. Lett. 79 (2001), no. 6, 281-284.
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FORMULA
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[seq(op(PermUnrank3R(j)), j=0..)]; (Maple code given below)
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EXAMPLE
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In this table each row consists of A001563[n] permutations of (n+1) terms; i.e. we have (1/) 2,1/ 1,3,2; 3,1,2; 3,2,1; 2,3,1/ 1,2,4,3; 2,1,4,3;
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,...
3,1,2/4,5,6,7,8,9,...
3,2,1/4,5,6,7,8,9,...
2,3,1/4,5,6,7,8,9,...
1,2,4,3/5,6,7,8,9,...
2,1,4,3/5,6,7,8,9,...
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MAPLE
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with(group); permul := (a, b) -> mulperms(b, a); PermUnrank3R := proc(r) local n; n := nops(factorial_base(r)); convert(PermUnrank3Raux(n+1, r, []), 'permlist', 1+(((r+2) mod (r+1))*n)); end; PermUnrank3Raux := proc(n, r, p) local s; if(0 = r) then RETURN(p); else s := floor(r/((n-1)!)); RETURN(PermUnrank3Raux(n-1, r-(s*((n-1)!)), permul(p, [[n, n-s]]))); fi; end;
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CROSSREFS
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A060119 = Positions of these permutations in the "canonical list" A055089 (where also the rest of procedures can be found). A060118 gives position of the inverse permutation of each, and A065183 positions after Foata transform.
Inversion vectors: A064039.
Cf. A060125, A060128-A060131, A060132, A060495.
Sequence in context: A049456 A117506 A055089 this_sequence A112592 A070036 A059779
Adjacent sequences: A060114 A060115 A060116 this_sequence A060118 A060119 A060120
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen Mar 02 2001
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