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A055091 Minimum number of transpositions needed to represent each permutation given in reversed colexicographic ordering A055089. 9
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 (list; graph; refs; listen; history; text; internal format)
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 * A014678 A164516 A016533

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

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Last modified December 6 04:14 EST 2019. Contains 329784 sequences. (Running on oeis4.)