login
Number of permutations of n elements whose unsigned reversal distance is k.
0

%I #12 Feb 24 2020 04:26:28

%S 1,1,1,1,3,2,1,6,15,2,1,10,51,56,2,1,15,127,390,185,2,1,21,263,1562,

%T 2543,648,2,1,28,483,4635,16445,16615,2111,2,1,36,820,11407,69863,

%U 169034,105365,6352,2

%N Number of permutations of n elements whose unsigned reversal distance is k.

%C Probably an erroneous version of A300003. Some inner terms of the triangle differ slightly. Sean A. Irvine reread the paper and checked manually that a(13) should be 52. The last row 1, 36, 820 ... 6352, 2 was added later and is ok. - _Georg Fischer_, Feb 24 2020

%H J. D. Kececioglu, and D. Sankoff, <a href="https://www.researchgate.net/publication/226954865_Exact_and_Approximation_Algorithms_for_Sorting_by_Reversals_with_Application_to_Genome_Rearrangement">Exact and approximation algorithms for sorting by reversals, with application to genome rearrangement</a>, Algorithmica (1995) 13:180.

%e a(3,1) = 3 because the only three permutations of S_3 that require exactly one reversal to be sorted are (1 3 2), (2 1 3) and (3 2 1).

%Y Cf. A300003.

%K nonn,tabl

%O 1,5

%A _Anthony Labarre_, Mar 29 2006, Jun 03 2006