摘要翻译：
在南印度，有一种传统的圆点线画模式，称为“kolam”，其中单线画或“无限kolam”提供了非常有趣的数学问题。例如，我们解决以下简单的问题：对于给定的点网格模式，我们可以绘制多少个无限Kolam模式？最简单的方法是在判断是否为无限大的Kolam的同时画出Kolam的可能模式。这样的搜索问题似乎是NP完全的。然而，它肯定不是。本文主要研究了点阵的菱形网格（1-3-5-3-1）和（1-3-5-7-5-3-1）。通过对无穷大Kolam的纽结理论描述，我们给出了如何找到解，从而不可避免地给出了无穷大Kolam不是NP完全的陈述的证明简图。它的进一步讨论将在最后一节中给出。
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英文标题：
《Solving Infinite Kolam in Knot Theory》
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作者：
Yukitaka Ishimoto
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最新提交年份：
2007
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Discrete Mathematics        离散数学
分类描述：Covers combinatorics, graph theory, applications of probability. Roughly includes material in ACM Subject Classes G.2 and G.3.
涵盖组合学，图论，概率论的应用。大致包括ACM学科课程G.2和G.3中的材料。
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一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  In south India, there are traditional patterns of line-drawings encircling dots, called ``Kolam'', among which one-line drawings or the ``infinite Kolam'' provide very interesting questions in mathematics. For example, we address the following simple question: how many patterns of infinite Kolam can we draw for a given grid pattern of dots? The simplest way is to draw possible patterns of Kolam while judging if it is infinite Kolam. Such a search problem seems to be NP complete. However, it is certainly not. In this paper, we focus on diamond-shaped grid patterns of dots, (1-3-5-3-1) and (1-3-5-7-5-3-1) in particular. By using the knot-theory description of the infinite Kolam, we show how to find the solution, which inevitably gives a sketch of the proof for the statement ``infinite Kolam is not NP complete.'' Its further discussion will be given in the final section.
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PDF链接：
https://arxiv.org/pdf/710.1976