论文标题
有限场上的对称多项式
Symmetric polynomials over finite fields
论文作者
论文摘要
结果表明，如果每个基本对称的$ p^k，2p^k，2p^k，\ dots，（q-1）p^k $，$ k $ k = 0,1,1,2,2，\ d dots $ conthyme $ p^k，$ k = 0,1,2,2，\ d d octos $ a n of Symortric Group的自然作用，则有限$ q $ e元素$ q $ e元素属于同一轨道的两个向量属于同一轨道。当$ q = p $且尺寸较大时，与对称组的自然置换表示形式相比，对称组的自然排列表示的一组分离的多项式不变性不远。得出了$ q $元素的字段上相对较小的多项式多项式分离集。
It is shown that two vectors with coordinates in the finite $q$-element field of characteristic $p$ belong to the same orbit under the natural action of the symmetric group if each of the elementary symmetric polynomials of degree $p^k,2p^k,\dots,(q-1)p^k$, $k=0,1,2,\dots$ has the same value on them. This separating set of polynomial invariants for the natural permutation representation of the symmetric group is not far from being minimal when $q=p$ and the dimension is large compared to $p$. A relatively small separating set of multisymmetric polynomials over the field of $q$ elements is derived.
