关于柱凸和凸Carlitz多项式
On column-convex and convex Carlitz polyominoes
摘要：
本文引入并研究了{ \it Carlitz多项式}。特别是，我们表明，随着$n$增长到无穷大，渐近的数量\begin{enumerate} \item column-convex Carlitz polyominoes with perimeter $2n$ is \beq \frac{9\sqrt{2}(14+3\sqrt{3})}{2704\sqrt{πn^3}}4^n. \feq \item convex Carlitz polyominoes with perimeter $2n$ is \beq \frac{n+1}{10}\left(\frac{3+\sqrt{5}}{2}\right)^{n-2}. \feq \end{enumerate}
英文摘要：
In this paper, we introduce and study {\it Carlitz polyominoes}. In particular, we show that, as $n$ grows to infinity, asymptotically the number of \begin{enumerate} \item column-convex Carlitz polyominoes with perimeter $2n$ is \beq \frac{9\sqrt{2}(14+3\sqrt{3})}{2704\sqrt{πn^3}}4^n. \feq \item convex Carlitz polyominoes with perimeter $2n$ is \beq \frac{n+1}{10}\left(\frac{3+\sqrt{5}}{2}\right)^{n-2}. \feq \end{enumerate}
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