Taking a combinatorial point of view on cyclotomic polynomials leads to a larger class of polynomials we shall call the inclusion-exclusion polynomials. This gives a more appropriate setting for certain types of questions about the coefficients of these polynomials. After establishing some basic properties of inclusion-exclusion polynomials we turn to a detailed study of the structure of ternary inclusion-exclusion polynomials. The latter subclass is exemplified by cyclotomic polynomials Φpqr, where p < q < r are odd primes. Our main result is that the set of coefficients of Φpqr is simply a string of consecutive integers which depends only on the residue class of r modulo pq.
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