English

Counting decomposable multivariate polynomials

Commutative Algebra 2009-07-02 v2 Combinatorics

Abstract

A polynomial f (multivariate over a field) is decomposable if f = g(h) with g univariate of degree at least 2. We determine the dimension (over an algebraically closed field) of the set of decomposables, and an approximation to their number over a finite field. The relative error in our approximations is exponentially decaying in the input size.

Keywords

Cite

@article{arxiv.0811.4726,
  title  = {Counting decomposable multivariate polynomials},
  author = {Joachim von zur Gathen},
  journal= {arXiv preprint arXiv:0811.4726},
  year   = {2009}
}

Comments

v2: 21 pages, simplification in the proof of Theorem 4.1

R2 v1 2026-06-21T11:46:22.655Z