Geodesic
Nonintersecting Lattice Paths on the Cylinder
Séminaire lotharingien de combinatoire, Tome 52 (2004-2007)

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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". 

@article{SLC_2004-2007_52_a1,
     author = {Markus Fulmek},
     title = {Nonintersecting {Lattice} {Paths} on the {Cylinder}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {52},
     year = {2004-2007},
     url = {http://geodesic.mathdoc.fr/item/SLC_2004-2007_52_a1/}
}
TY  - JOUR
AU  - Markus Fulmek
TI  - Nonintersecting Lattice Paths on the Cylinder
JO  - Séminaire lotharingien de combinatoire
PY  - 2004-2007
VL  - 52
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2004-2007_52_a1/
ID  - SLC_2004-2007_52_a1
ER  - 
%0 Journal Article
%A Markus Fulmek
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%J Séminaire lotharingien de combinatoire
%D 2004-2007
%V 52
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2004-2007_52_a1/
%F SLC_2004-2007_52_a1
Markus Fulmek. Nonintersecting Lattice Paths on the Cylinder. Séminaire lotharingien de combinatoire, Tome 52 (2004-2007). http://geodesic.mathdoc.fr/item/SLC_2004-2007_52_a1/