11 citations · 44 across the 10 of their papers we have counts for
6 papers · 1 filter
Survey on counting special types of polynomials
Joachim von zur Gathen, Konstantin Ziegler
Most integers are composite and most univariate polynomials over a finite field are reducible. The Prime Number Theorem and a classical result of Gauß count the remaining ones, app…
Normal form for Ritt's Second Theorem
Joachim von zur Gathen
Ritt's Second Theorem deals with composition collisions g o h = g* o h* of univariate polynomials over a field, where deg g = deg h*. Joseph Fels Ritt (1922) presented two types of…
Compositions and collisions at degree p^2
Raoul Blankertz, Joachim von zur Gathen, Konstantin Ziegler
A univariate polynomial f over a field is decomposable if f = g o h = g(h) for nonlinear polynomials g and h. In order to count the decomposables, one wants to know, under a suitab…
Composition collisions and projective polynomials
Joachim von zur Gathen, Mark Giesbrecht, Konstantin Ziegler
The functional decomposition of polynomials has been a topic of great interest and importance in pure and computer algebra and their applications. The structure of compositions of…
Counting reducible, powerful, and relatively irreducible multivariate polynomials over finite fields
Joachim von zur Gathen, Alfredo Viola, Konstantin Ziegler
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…
Counting decomposable univariate polynomials
Joachim von zur Gathen
A univariate polynomial f over a field is decomposable if it is the composition f = g(h) of two polynomials g and h whose degree is at least 2. We determine the dimension (over an…