Skip to Main content Skip to Navigation
Journal articles

On Hultman numbers

Abstract : Finding a sequence of transpositions that transforms a given permutation into the identity permutation and is of the shortest possible length is an important problem in bioinformatics. Here, a transposition consists in exchanging two contiguous intervals of the permutation. Bafna and Pevzner introduced the cycle graph as a tool for working on this problem. In particular, they took advantage of the decomposition of the cycle graph into so-called alternating cycles. Later, Hultman raised the question of determining the number of permutations with a cycle graph containing a given quantity of alternating cycles. The resulting number is therefore similar to the Stirling number of the first kind. We provide an explicit formula for computing what we call the Hultman numbers, and give a few numerical values. We also derive formulae for related cases, as well as for a much more general problem. Finally, we indicate a counting result related to another operation on permutations called the "block-interchange".
Document type :
Journal articles
Complete list of metadatas

Cited literature [11 references]  Display  Hide  Download

https://hal-upec-upem.archives-ouvertes.fr/hal-00728923
Contributor : Anthony Labarre <>
Submitted on : Friday, September 7, 2012 - 9:08:17 AM
Last modification on : Thursday, June 4, 2020 - 10:24:03 AM
Long-term archiving on: : Saturday, December 8, 2012 - 3:40:00 AM

File

jis2007.pdf
Publisher files allowed on an open archive

Identifiers

  • HAL Id : hal-00728923, version 1

Collections

Citation

Jean-Paul Doignon, Anthony Labarre. On Hultman numbers. Journal of Integer Sequences, University of Waterloo, 2007, 10 (6), pp.13. ⟨hal-00728923⟩

Share

Metrics

Record views

115

Files downloads

107