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%I #18 Feb 16 2020 00:59:02
%S 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,
%T 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,
%U 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
%N A list of all finite permutations in "PermUnrank3R" ordering. (Inverses of the permutations of A060118.)
%C PermUnrank3R and PermUnrank3L are slight modifications of unrank2 algorithm presented in Myrvold-Ruskey article.
%H W. Myrvold and F. Ruskey, <a href="https://doi.org/10.1016/S0020-0190(01)00141-7">Ranking and Unranking Permutations in Linear Time</a>, Inform. Process. Lett. 79 (2001), no. 6, 281-284.
%F [seq(op(PermUnrank3R(j)), j=0..)]; (Maple code given below)
%e 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;
%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 3,1,2/4,5,6,7,8,9,...
%e 3,2,1/4,5,6,7,8,9,...
%e 2,3,1/4,5,6,7,8,9,...
%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); 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;
%Y 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.
%Y Inversion vectors: A064039.
%Y Cf. A060125, A060128, A060129, A060130, A060131, A060132, A060495.
%K nonn,tabf
%O 0,2
%A _Antti Karttunen_, Mar 02 2001
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