Séminaire Lotharingien de Combinatoire, B52b (2004), 16 pp.
Nonintersecting Lattice Paths on the Cylinder
We show how a formula concerning "vicious walkers" (which basically are
nonintersecting lattice paths) on the cylinder
given by P. J. Forrester can be proved and generalized
by using the Lindström-Gessel-Viennot method,
after having things set up in the
right way. We apply the corresponding results to the
(thermodynamic limit of the) free energy of the "lock step
model of vicious walkers," thus completing (and in one instance correcting)
the work of Forrester.
Moreover, we also show how a related formula given
by I. Gessel and C. Krattenthaler can be obtained from the same
"point of view".
Received: April 7, 2004.
Final Version: August 16, 2004.
Accepted: September 14, 2004.
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