置换的全圈表示
A Representation of Permutations with Full Cycle
摘要：
当q > 2时，Carlitz证明了F_q上的置换多项式群（PP）是由线性多项式和x^{q-2}生成的。在此基础上，本文给出了表示素域F_p上所有满圈PP的一种简单方法，其中p是奇素数。利用p元对称群S_p与F_p上PP群的同构，以及S_p中置换具有相同圈结构的充要条件是它们是共轭的.
英文摘要：
For q > 2, Carlitz proved that the group of permutation polynomials (PPs) over F_q is generated by linear polynomials and x^{q-2}. Based on this result, this note points out a simple method for representing all PPs with full cycle over the prime field F_p, where p is an odd prime. We use the isomorphism between the symmetric group S_p of p elements and the group of PPs over F_p, and the well-known fact that permutations in S_p have the same cycle structure if and only if they are conjugate.
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。
