Vol. 7, No. 4, 2014

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Distribution of genome rearrangement distance under double cut and join

Jackie Christy, Josh McHugh, Manda Riehl and Noah Williams

Vol. 7 (2014), No. 4, 491–507
Abstract

Using the double-cut-and-join (DCJ) model for genome rearrangement we use combinatorial techniques to analyze the distribution of genomes under DCJ distance. We present an exponential generating function for the number of genomes that are maximally distant from a given genome and provide a formula for the number of genomes that are any given distance from an arbitrary starting genome.

Keywords
genome rearrangement, double cut and join, generating function
Mathematical Subject Classification 2010
Primary: 05E05, 68R15
Milestones
Received: 14 December 2012
Revised: 30 March 2013
Accepted: 1 April 2013
Published: 31 May 2014

Communicated by Anant Godbole
Authors
Jackie Christy
Department of Mathematics
University of Wisconsin
Eau Claire, WI 54702-4004
United States
Josh McHugh
Department of Mathematics
University of Wisconsin
Eau Claire, WI 54702-4004
United States
Manda Riehl
Department of Mathematics
University of Wisconsin
Eau Claire, WI 54702-4004
United States
Noah Williams
Department of Mathematics 340
University of Colorado
Campus Box 395
Boulder, CO 80309-0395
United States