Abstract
We present an analytical technique for counting exactly the number of ways of embedding a graph in a fairly general family of self-similar deterministic fractals. As a result, series expansion for statistical systems can be obtained that are exact order by order in the expansion parameter. As an illustration, series expansions for self-avoiding walks on a Sierpriaanski carpet are given. Analytical results for systems on infinitely ramified fractals are obtained in the thermodynamic limit without making any approximation on the lattice.
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