论文标题
二项式系数和未签名的Stirl数字的基质产品
Matrix products of binomial coefficients and unsigned Stirling numbers
论文作者
论文摘要
我们研究$ \ sum_ {k = m}^n a_ {nk} b_ {km} $的形式的总和，其中$ a_ {nk} $和$ b_ {km {km} $是二项式系数或无符号的stirl stirling数字。在少数情况下，它们可以以封闭形式书写。失败的总和仍然具有许多共同的特征：组合解释，类似帕斯卡的复发，与签名版本的逆关系以及作为多项式碱基之间变化系数的解释。
We study sums of the form $\sum_{k=m}^n a_{nk} b_{km}$, where $a_{nk}$ and $b_{km}$ are binomial coefficients or unsigned Stirling numbers. In a few cases they can be written in closed form. Failing that, the sums still share many common features: combinatorial interpretations, Pascal-like recurrences, inverse relations with their signed versions, and interpretations as coefficients of change between polynomial bases.
