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A060117 A list of all finite permutations in "PermUnrank3R" ordering. (Inverses of the permutations of A060118.) 53
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; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
PermUnrank3R and PermUnrank3L are slight modifications of unrank2 algorithm presented in Myrvold-Ruskey article.
LINKS
W. Myrvold and F. Ruskey, Ranking and Unranking Permutations in Linear Time, Inform. Process. Lett. 79 (2001), no. 6, 281-284.
FORMULA
[seq(op(PermUnrank3R(j)), j=0..)]; (Maple code given below)
EXAMPLE
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 number 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,...
MAPLE
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;
CROSSREFS
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.
Sequence in context: A179205 A055089 A363086 * A196526 A234504 A112592
KEYWORD
nonn,tabf
AUTHOR
Antti Karttunen, Mar 02 2001
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)