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 A060118 A list of all finite permutations in "PermUnrank3L" ordering. (Inverses of the permutations of A060117.) 39
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified March 31 14:42 EDT 2023. Contains 361663 sequences. (Running on oeis4.)