【摘要】 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.更多还原

【Abstract】 Let Fq be afinite field with q elements,where q is apower of aprime and Fn qbe the n-dimensional row vector space,and denote the Gaussian coefficient by[nm] q which as numbers of subspaces 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.更多还原