Séminaire Lotharingien de Combinatoire, B52b (2004), 16 pp.

Markus Fulmek

Nonintersecting Lattice Paths on the Cylinder

Abstract. 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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