用组合方法证明Gaussian系数恒等式

Proof of Gaussian Coefficient Identities from Combinatorial Method

设F_q是q个元素的有限域,其中q是素数的幂,F_q^n是F_q上n维向量空间,用[n/m]_q表示Gaussian系数,它可看作为F_q^n的m维子空间的个数.用组合方法证明了几个Gaussian系数恒等式.

Let Fq be a finit field with q elements, where q is a pawer of a prime and Fq^n be the n-dimensional row vector space, and denote the Gaussian coefficient by [m^n] q which as numbers of subspaces over Fq. Some Gauusian coefficient identical relations are proved by the combinatorial method.