Vol. 5, No. 2, 2012

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Commutation classes of double wiring diagrams

Patrick Dukes and Joe Rusinko

Vol. 5 (2012), No. 2, 207–218
Abstract

We describe a new method for computing the graph of commutation classes of double wiring diagrams. Using these methods we compute the graph for five strings or less which allows us to confirm a positivity conjecture of Fomin and Zelevinsky when n 4.

Keywords
wiring diagram, matrix positivity, Laurent phenomenon
Mathematical Subject Classification 2010
Primary: 05E15
Secondary: 15B48
Milestones
Received: 30 August 2011
Revised: 3 September 2011
Accepted: 14 September 2011
Published: 27 January 2013

Communicated by Ravi Vakil
Authors
Patrick Dukes
School of Computing
Clemson University
Clemson, SC 29634
United States
Joe Rusinko
Department of Mathematics
Winthrop University
Rock Hill, SC 29733
United States