This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A060117 #18 Feb 16 2020 00:59:02 %S A060117 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 A060117 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 A060117 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 A060117 A list of all finite permutations in "PermUnrank3R" ordering. (Inverses of the permutations of A060118.) %C A060117 PermUnrank3R and PermUnrank3L are slight modifications of unrank2 algorithm presented in Myrvold-Ruskey article. %H A060117 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 A060117 [seq(op(PermUnrank3R(j)), j=0..)]; (Maple code given below) %e A060117 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 A060117 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 A060117 1/2,3,4,5,6,7,8,9,... %e A060117 2,1/3,4,5,6,7,8,9,... %e A060117 1,3,2/4,5,6,7,8,9,... %e A060117 3,1,2/4,5,6,7,8,9,... %e A060117 3,2,1/4,5,6,7,8,9,... %e A060117 2,3,1/4,5,6,7,8,9,... %e A060117 1,2,4,3/5,6,7,8,9,... %e A060117 2,1,4,3/5,6,7,8,9,... %p A060117 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 A060117 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 A060117 Inversion vectors: A064039. %Y A060117 Cf. A060125, A060128, A060129, A060130, A060131, A060132, A060495. %K A060117 nonn,tabf %O A060117 0,2 %A A060117 _Antti Karttunen_, Mar 02 2001