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

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, 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, 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

Offset

0,4

Links

Antti Karttunen, Table of n, a(n) for n = 0..40320

Index entries for sequences related to factorial base representation

Formula

a(n) = A055093(n) - A055090(n).

a(n) = A046660(A290095(n)) = A060130(A060126(n)). - Antti Karttunen, Dec 30 2017

Maple

with(group); [seq(count_transpositions(convert(PermRevLexUnrank(j), 'disjcyc')), j=0..)];
count_transpositions := proc(l) local c, t; t := 0; for c in l do t := t + (nops(c)-1); od; RETURN(t); end;
# Procedure PermRevLexUnrank given in A055089.

Crossrefs

Cf. A046660, A055089, A055090, A055093, A060130, A290095.

Cf. also A034968 (minimum number of adjacent transpositions).

Sequence in context: A318439 A106180 A274369 * A332380 A014678 A332381

Adjacent sequences: A055088 A055089 A055090 * A055092 A055093 A055094

Keyword

nonn

Author

Antti Karttunen, Apr 18 2000

Extensions

Entry revised by Antti Karttunen, Dec 30 2017

Status

approved