可分解一元多项式的计数
Counting decomposable univariate polynomials
摘要：
域上的一元多项式f是可分解的，如果它是两个次数至少为2的多项式g和h的复合f = g（h）。我们确定的维度（在一个代数闭域）的一组可分解的，和一个近似的数量超过一个有限域。驯服的情况下，场特性p不划分的程度n的f，是合理的理解，我们得到指数下降的误差界。在p整除n的情况下，更具有挑战性，我们的误差界更弱。
英文摘要：
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 algebraically closed field) of the set of decomposables, and an approximation to their number over a finite field. The tame case, where the field characteristic p does not divide the degree n of f, is reasonably well understood, and we obtain exponentially decreasing error bounds. The wild case, where p divides n, is more challenging and our error bounds are weaker.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
