A164645 Triangle read by rows: a(n,k) is the number of permutations of n elements with prefix transposition distance equal to k.

1, 1, 1, 1, 3, 2, 1, 6, 14, 3, 1, 10, 50, 55, 4, 1, 15, 130, 375, 194, 5, 1, 21, 280, 1575, 2598, 562, 3, 1, 28, 532, 4970, 18096, 15532, 1161, 0, 1, 36, 924, 12978, 85128, 188386, 74183, 1244, 0, 1, 45, 1500, 29610, 308988, 1364710, 1679189, 244430, 327

Offset: 1

Author

Anthony Labarre, Aug 19 2009

Keywords

• nonn
• tabl

Comments

A prefix transposition refers to the displacement of the first f elements of the permutation. The prefix transposition distance is the minimum number of such moves required to transform a given permutation into the identity permutation.

Examples

			a(4,2)=3 because the only 3 permutations that require 2 prefix transpositions to be sorted are (1 4 3 2), (2 1 4 3) and (4 3 2 1)
		

References

• Zanoni Dias and Joao Meidanis, Sorting by Prefix Transpositions, Proceedings of the Ninth International Symposium on String Processing and Information Retrieval (SPIRE), 2002, 65-76, vol. 2476 of Lecture Notes in Computer Science, Springer-Verlag
• G. Fertin, A. Labarre, I. Rusu, E. Tannier, and S. Vialette, "Combinatorics of genome rearrangements", The MIT Press, 2009, page 37.

Links

• G. Fertin, A. Labarre, I. Rusu, E. Tannier, and S. Vialette, "Combinatorics of genome rearrangements", The MIT Press, 2009.