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A065603 Transposition diameter: maximal number of moves in an optimal sorting of n objects by moving blocks. 2
0, 1, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 8, 8, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Arises in sorting cards in a bridge hand; also in computational biology because block move is a fundamental type of mutation, called transposition.

R. de A. Hausen et al. showed that 9 <= a(16) <= 10.

LINKS

Table of n, a(n) for n=1..15.

H. Eriksson et al., Sorting a bridge hand, Discrete Math., 241 (2001), 289-300.

R. de A. Hausen, L. Faria, C. M. H. de Figueiredo, and L. A. B. Kowada, On the toric graph as a tool to handle the problem of sorting by transpositions, LNCS 5167 (2008), 79-91. doi:10.1007/978-3-540-85557-6_8

J. Gonçalves, L. R. Bueno, R. A. Hausen, Assembling a New and Improved Transposition Distance Database, in Simpósio Brasileiro de Pesquisa Operacional, Sept. 2013.

Index entries for sequences related to sorting

FORMULA

It is conjectured that a(n) = ceiling((n+1)/2) for n >= 3 except for n = 13 and 15.

CROSSREFS

Cf. A164366, A219243

Sequence in context: A120835 A091374 A266977 * A225215 A214672 A268060

Adjacent sequences:  A065600 A065601 A065602 * A065604 A065605 A065606

KEYWORD

nonn,nice,more,hard

AUTHOR

N. J. A. Sloane, Dec 02 2001

EXTENSIONS

Definition corrected by Peter Lipp, Dec 16 2008

Edited by Max Alekseyev, Nov 07 2011

STATUS

approved

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Last modified July 23 00:43 EDT 2019. Contains 325228 sequences. (Running on oeis4.)