Counting Reducible, Powerful, and Relatively Irreducible Multivariate Polynomials over Finite Fields
Counting Reducible, Powerful, and Relatively Irreducible Multivariate Polynomials over Finite Fields
We present counting methods for some special classes of multivariate polynomials over a finite field, namely, the reducible ones, the $s$-powerful ones (divisible by the $s$th power of a nonconstant polynomial), and the relatively irreducible ones (irreducible but reducible over an extension field). One approach employs generating functions, and another …