For a nonnegative integer $n$, and a prime $\wp$ in $\mathbb{F}_q[T]$, weprove a result that provides a method for computing the number of integers $m$with $0 \le m \le n$ for which the Carlitz binomial coefficients$\binom{n}{m}_C$ fall into each of the residue classes modulo $\wp$. Our mainresult can be viewed as a function field analogue of the Garfield-Wilf theorem.
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机译:对于非负整数$ n $和$ \ mathbb {F} _q [T] $中的质数$ \ wp $,我们证明了一个结果,该结果提供了一种计算$ 0 \ le m \的整数$ m $数量的方法。 ,其中Carlitz二项式系数$ \ binom {n} {m} _C $属于每个残元类,取模$ \ wp $为模。我们的主要结果可以看作是Garfield-Wilf定理的函数域类似物。
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