$p$元拍卖函数的多项式表示
Polynomial expressions of $p$-ary auction functions
摘要：
设$\mathbb{F}_p$是素数阶有限域$p$ .对于任何函数$f \colon \mathbb{F}_p{}^n \to \mathbb{F}_p$，在$\mathbb{F}_p$上存在唯一的多项式，其关于与$f$一致的每个变量的次数至多为$p-1$。我们称之为$f$的极小多项式。一般来说，找到给定函数的极小多项式的具体表达式是一项非平凡的任务，在文献中仅对有限的函数类进行了计算。本文研究了与拍卖、投票等实际过程密切相关的几个函数的极小多项式表达式。
英文摘要：
Let $\mathbb{F}_p$ be the finite field of prime order $p$. For any function $f \colon \mathbb{F}_p{}^n \to \mathbb{F}_p$, there exists a unique polynomial over $\mathbb{F}_p$ having degree at most $p-1$ with respect to each variable which coincides with $f$. We call it the minimal polynomial of $f$. It is in general a non-trivial task to find a concrete expression of the minimal polynomial of a given function, which has only been worked out for limited classes of functions in the literature. In this paper, we study minimal polynomial expressions of several functions that are closely related to some practically important procedures such as auction and voting.
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。
