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%I #11 Feb 16 2020 00:59:29
%S 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,
%T 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,
%U 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
%N A list of all finite permutations in "PermUnrank3L" ordering. (Inverses of the permutations of A060117.)
%C 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.
%F [seq(op(PermUnrank3L(j)), j=0..)]; (Maple code given below)
%e In this table each row consists of A001563[n] permutations of (n+1) terms;
%e 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:
%e 1/2,3,4,5,6,7,8,9,...
%e 2,1/3,4,5,6,7,8,9,...
%e 1,3,2/4,5,6,7,8,9,...
%e 2,3,1/4,5,6,7,8,9,...
%e 3,2,1/4,5,6,7,8,9,...
%e 3,1,2/4,5,6,7,8,9,...
%e 1,2,4,3/5,6,7,8,9,...
%e 2,1,4,3/5,6,7,8,9,...
%p 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;
%Y A060120 = Positions of these permutations in the "canonical list" A055089. Cf. also A060117.
%K nonn,tabf
%O 0,2
%A _Antti Karttunen_, Mar 02 2001
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