论文标题
计算格子三角：组合学中的弗雷德尔姆方程
Counting lattice triangulations: Fredholm equations in combinatorics
论文作者
论文摘要
令$ f（m，n）$为$ m \ times n $矩形的原始晶格三角形的数量。我们计算限制$ \ lim_n f（m，n）^{1/n} $ for $ m = 2 $和$ 3 $。对于$ m = 2 $，我们获得了等于$（611+ \ sqrt {73}）/36 $的限制的确切值。对于$ M = 3 $，我们就某些Fredholm的积分方程式在生成功能方面表达了限制。这提供了用任何给定精度计算极限的多项式时间算法（与计算数字的数量相关的多项式）。
Let $f(m,n)$ be the number of primitive lattice triangulations of $m\times n$ rectangle. We compute the limits $\lim_n f(m,n)^{1/n}$ for $m=2$ and $3$. For $m=2$ we obtain the exact value of the limit which is equal to $(611+\sqrt{73})/36$. For $m=3$, we express the limit in terms of certain Fredholm's integral equation on generating functions. This provides a polynomial time algorithm for computation of the limit with any given precision (polynomial with respect the the number of computed digits).
