关于k-omino塔的enumeration
On the enumeration of k-omino towers
摘要：
我们描述了一类固定的polyominoes称为$k$ -omino塔，通过堆叠大小为$k\times 1$的矩形块上的凸基地组成的这些相同的$k$-omino块。通过对具有固定面积的$kn$的$k$ -omino塔集进行划分，给出了$k$ -omino塔集的一个递推式，从而证明了$k$ -omino塔集是由一个高斯超几何函数枚举的.在这种情况下的证明意味着一个更一般的超几何身份与参数类似的经典结果库默尔。
英文摘要：
We describe a class of fixed polyominoes called $k$-omino towers that are created by stacking rectangular blocks of size $k\times 1$ on a convex base composed of these same $k$-omino blocks. By applying a partition to the set of $k$-omino towers of fixed area $kn$, we give a recurrence on the $k$-omino towers therefore showing the set of $k$-omino towers is enumerated by a Gauss hypergeometric function. The proof in this case implies a more general hypergeometric identity with parameters similar to those given in a classical result of Kummer.
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