A060118 A list of all finite permutations in "PermUnrank3L" ordering. (Inverses of the permutations of A060117.)

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

Offset

0,2

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.

Links

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

Formula

[seq(op(PermUnrank3L(j)), j=0..)]; (Maple code given below)

Example

In this table each row consists of A001563[n] permutations of (n+1) terms;
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,...
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,...

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;

Crossrefs

A060120 = Positions of these permutations in the "canonical list" A055089. Cf. also A060117.

Sequence in context: A111867 A326036 A133776 * A329143 A219032 A234567

Adjacent sequences: A060115 A060116 A060117 * A060119 A060120 A060121

Keyword

nonn,tabf

Author

Antti Karttunen, Mar 02 2001

Status

approved