A060117 A list of all finite permutations in "PermUnrank3R" ordering. (Inverses of the permutations of A060118.)

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

Offset

0,2

Comments

PermUnrank3R and PermUnrank3L are slight modifications of unrank2 algorithm presented in Myrvold-Ruskey article.

Links

Table of n, a(n) for n=0..104.

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.

Cf. A060125, A060128, A060129, A060130, A060131, A060132, A060495.

Sequence in context: A055089 A363086 A378881 * A196526 A234504 A112592

Adjacent sequences: A060114 A060115 A060116 * A060118 A060119 A060120

Keyword

nonn,tabf

Author

Antti Karttunen, Mar 02 2001

Status

approved