Counting reducible, powerful, and relatively irreducible multivariate polynomials over finite fields

Abstract

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, another one uses a combinatorial method. They yield exact formulas and approximations with relative errors that essentially decrease exponentially in the input size.

to appear in SIAM Journal on Discrete Mathematics

References in corpus (3)

• Indecomposable polynomials and their spectrum
• The number of reducible space curves over a finite field
• Number of irreducible polynomials in several variables over finite fields

Cited by in corpus (2)

• Normal form for Ritt's Second Theorem
• The number of reducible space curves over a finite field