Abstract
In this chapter we begin by introducing a powerful combinatorial theorem due to Pólya. This result is applied to switching theory to produce a number of different classifications. Specifically, we count the number of equivalence classes under the following notions of equivalence: (1) complementation of some of the variables, (2) permutation of some of the variables, (3) complementations and/or permutations of the variables, (4) any linear function of the variables, (5) any affine function of the variables. We obtain cycle index polynomials in all cases above. This leads to the desired numbers which are tabulated. A generalization of the Pólya result by DeBruijn is considered next. Applications are made which allow us to include negation of functions as part of the definition of equivalence. In this manner we obtain the number of genera and the number of equivalence classes of networks.
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