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The perimeter and area generating functions of exactly solvable polygonmodels satisfy q-functional equations, where q is the area variable. Thebehaviour in the vicinity of the point where the perimeter generating functiondiverges can often be described by a scaling function. We develop the method ofq-linear approximants in order to extract the approximate scaling behaviour ofpolygon models when an exact solution is not known. We test the validity of ourmethod by approximating exactly solvable q-linear polygon models. This leads toscaling functions for a number of q-linear polygon models, notably generalizedrectangles, Ferrers diagrams, and stacks.Comment: 17 pages, 3 figure

q-linear approximants: scaling functions for polygon models