Independence polynomials of circulants with an application to music

The independence polynomial of a graph G is the generating function I(G,x)[email protected]?"k">="0i"kx^k, where i"k is the number of independent sets of cardinality k in G. We show that the problem of evaluating the independence polynomial of a graph at any fixed non-zero number is intractable, even when restricted to circulants. We provide a formula for the independence polynomial of a certain family of circulants, and its complement. As an application, we derive a formula for the number of chords in an n-tet musical system (one where the ratio of frequencies in a semitone is 2^1^/^n) without 'close' pitch classes.

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