某些置换群多项式的枚举
Enumeration of certain permutation group polynomials
AI总结：
该研究在奇特征有限域上构造新的置换群多项式，确定其等价多项式数量，并解决Hasan和Kumar（2026）提出的各类及等价置换群多项式的枚举问题。
AI中文摘要：
我们在奇特征有限域上构造了一类新的置换群多项式，并明确给出其伴随多项式。此外，我们精确确定了该形式的置换群多项式数量，以及与该新族等价的置换群多项式数量。另外，我们完全解决了Hasan和Kumar（2026）提出的各类形式置换群多项式的枚举问题，以及与这些族等价的置换群多项式的枚举问题。
英文摘要：
We construct a new family of permutation group polynomials over finite fields of odd characteristic and explicitly provide its companion. Moreover, we precisely determine the number of permutation group polynomials of this form and those that are equivalent to this new family. In addition, we completely solve the problem of enumerating permutation group polynomials of the various forms presented in Hasan and Kumar (2026), as well as permutation group polynomials which are equivalent to these families.
