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%I #15 Dec 30 2017 10:00:29
%S 0,1,1,2,2,1,1,2,2,3,3,2,2,3,1,2,2,3,3,2,2,1,3,2,1,2,2,3,3,2,2,3,3,4,
%T 4,3,3,4,2,3,3,4,4,3,3,2,4,3,2,3,3,4,4,3,1,2,2,3,3,2,2,3,3,4,4,3,3,2,
%U 4,3,3,4,3,4,2,3,3,4,2,3,1,2,2,3,3,4,2,3,3,4,4,3,3,4,2,3,4,3,3,2,4,3,3,2,2
%N Minimum number of transpositions needed to represent each permutation given in reversed colexicographic ordering A055089.
%H Antti Karttunen, <a href="/A055091/b055091.txt">Table of n, a(n) for n = 0..40320</a>
%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%F a(n) = A055093(n) - A055090(n).
%F a(n) = A046660(A290095(n)) = A060130(A060126(n)). - _Antti Karttunen_, Dec 30 2017
%p with(group); [seq(count_transpositions(convert(PermRevLexUnrank(j),'disjcyc')),j=0..)];
%p count_transpositions := proc(l) local c,t; t := 0; for c in l do t := t + (nops(c)-1); od; RETURN(t); end;
%p # Procedure PermRevLexUnrank given in A055089.
%Y Cf. A046660, A055089, A055090, A055093, A060130, A290095.
%Y Cf. also A034968 (minimum number of adjacent transpositions).
%K nonn
%O 0,4
%A _Antti Karttunen_, Apr 18 2000
%E Entry revised by _Antti Karttunen_, Dec 30 2017
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