DiscoverCombinatorics and Statistical MechanicsCounting lattice paths with the kernel method
Counting lattice paths with the kernel method

Counting lattice paths with the kernel method

Update: 2008-05-09
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Models of directed paths have been used extensively in the scientific literature to model linear polymers. In this talk we examine directed path models of a linear polymer in various confining geometries.

We solve these models by showing that the generating function satisfies a functional equation and deriving formal solutions by using the kernel method.

While some generating functions are rational or algebraic, it turns out that in some interesting cases the generating functions are not differentiably finite.
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Counting lattice paths with the kernel method

Counting lattice paths with the kernel method

Cambridge University