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.
de A. Hausen et al. (2008) showed that 9 <= a(16) <= 10.
LINKS
V. Bafna and P. A. Pevzner, Sorting by transpositions, SIAM Journal on Discrete Mathematics, 11 (1998), 224-240.
V. Bafna and P. A. Pevzner, Sorting by transpositions, SIAM Journal on Discrete Mathematics, 11 (1998), 224-240.
H. Eriksson, K. Eriksson, J. Karlander, L. Svensson, and J. Wästlund, Sorting a bridge hand, Discrete Math. 241 (2001), 289-300.
H. Eriksson, K. Eriksson, J. Karlander, L. Svensson, and J. Wästlund, 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.
J. Gonçalves, L. R. Bueno, and R. A. Hausen, Assembling a New and Improved Transposition Distance Database, in Simpósio Brasileiro de Pesquisa Operacional, Sept. 2013.
FORMULA
It is conjectured that a(n) = ceiling((n+1)/2) for n >= 3 except for n = 13 and 15.
From Petros Hadjicostas, Dec 16 2019: (Start)
ceiling((n-1)/2) <= a(n) <= floor(3*n/4) for n >= 1 (Eriksson et al. (2001) state that these inequalities were proved in Bafna and Pevnzer (1998)).
ceiling((n+1)/2) <= a(n) <= floor((2*n-2)/3) for n >= 3 (see p. 293 in Eriksson et al. (2001)). (End)
CROSSREFS
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