Counting Monic Polynomials Without Prescribed Factors Over \(\mathbb{F}_q\)

In this short note we use the symbolic method to provide a brief proof for the ordinary generating function of the combinatorial class of monic polynomials over \(\mathbb{F}_q\) not divisible by anything from a given set of monic irreducibles.

Recommended citation: G. Wesley. "Counting Monic Polynomials Without Prescribed Factors Over \(\mathbb{F}_q\)" (2022). Local manuscript.
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