波利亚计数定理（英语：Pólya enumeration theorem，简称PET）用来研究不同着色方案的计数问题，它是组合数学中的一个重要的计数公式，是伯恩赛德引理的一般化，由乔治·波利亚在1937年的论文中提出并被广泛应用，该结果首先由John Howard Redfield在1927年发表，但当时很少有人能理解，十年后由波利亚独立重新发现。对于含n个对象的置换群G，用t种颜色着色的不同方案数为：

其中 为置换的循环指标（Cycle index）数目。

The Pólya enumeration theorem, also known as the Redfield–Pólya Theorem, is a theorem in combinatorics that both follows from and ultimately generalizes Burnside's lemma on the number of orbits of a group action on a set. The theorem was first published by John Howard Redfield in 1927. In 1937 it was independently rediscovered by George Pólya, who then greatly popularized the result by applying it to many counting problems, in particular to the enumeration of chemical compounds.