10 citations · 20 across the 6 of their papers we have counts for
6 papers
Counting invariant subspaces and decompositions of additive polynomials
Joachim von zur Gathen, Mark Giesbrecht, Konstantin Ziegler
The functional (de)composition of polynomials is a topic in pure and computer algebra with many applications. The structure of decompositions of (suitably normalized) polynomials f…
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…
Tame Decompositions and Collisions
Konstantin Ziegler
A univariate polynomial f over a field is decomposable if f = g o h = g(h) for nonlinear polynomials g and h. It is intuitively clear that the decomposable polynomials form a small…
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…