Exchange relations, Dyck paths and copolymer adsorption

Authors:
A. Rechnitzer;E. J. Janse van Rensburg
Affiliations:
Department of Mathematics, The University of Melbourne, Parkville, Victoria 3052, Australia;Department of Mathematics and Statistics, York University, Toronto, Ont., Canada M3J 1P3
Venue:
Discrete Applied Mathematics
Year:
2004

Citing 4
Cited 0

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Abstract

We consider a lattice model of fully directed copolymer adsorption equivalent to the enumeration of vertex-coloured Dyck paths. For two infinite families of periodie colourings we are able to solve the model exactly using a type of symmetry we call an exchange relation. For one of these families we are able to find an asymptotic expression for the location of the critical adsorption point as a function of the period of the colouring. This expression describes the effect of a regular inhomogeneity in the polymer on the adsorption transition.