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Exchange symmetries in Motzkin path and bargraph models of copolymer adsorption. (English) Zbl 1025.05002

Electron. J. Comb. 9, No. 1, Research paper R20, 24 p. (2002); printed version J. Comb. 9, No. 1 (2002).
This paper derives generating functions for various versions of the problem of random walks in a plane when the walk is never allowed to drop below a fixed line and backward steps are not allowed. Also the vertices or edges of the walk may be coloured.
The method used is described is an “exchange” method in which the generating function is divided up into a sum over various possible ways in which a walk can start.
Explicit formulae for the generating functions and critical activities are given for several models. 20 references.
Reviewer’s note: This technique seems to be new and useful, and capable of further development.

MSC:

05A15 Exact enumeration problems, generating functions
82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
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