几个恒等式及其组合方法的证明

Several identity and their combination method is proved

设Fq是q个元素的有限域,其中q是素数的幂,Fnq是Fq上n维向量空间,用[nm]q表示Gaussian系数,它可看做Fnq的m维子空间的个数.运用组合方法证明了几个已知的Gaussian系数恒等式,并给出几个新的Gaussian系数恒等式和它的组合方法证明.

Let Fq he a finite field with q elements, where q is a power of a prime and Fq be then-dimensional row vector space, and denote the Gaussian coefficient by[n m]q which as numbers ofsubspaces over Fq. First, proved several Gauusian coefficient identity with the combinatorial method, then several Gauusian coefficient identity are given and their proofs with the combinatorial method.