Title: On Hultman numbers
Authors: Doignon, Jean-Paul
Labarre, Anthony # ×
Issue Date: Jun-2007
Publisher: AT & T Corp.
Series Title: Journal of Integer Sequences vol:10 issue:6 pages:1-13
Article number: 07.6.2
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”.
ISSN: 1530-7638
Publication status: published
KU Leuven publication type: DI
Appears in Collections:Informatics Section
× corresponding author
# (joint) last author

Files in This Item:
File Description Status SizeFormat
jis2007.pdfMain article Published 193KbAdobe PDFView/Open


All items in Lirias are protected by copyright, with all rights reserved.