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 A055091 Minimum number of transpositions needed to represent each permutation given in reversed colexicographic ordering A055089. 9

%I

%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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Last modified January 19 12:36 EST 2020. Contains 331049 sequences. (Running on oeis4.)