Data and code from: Random knotting in very long off-lattice self-avoiding polygons

We present experimental results on knotting in off-lattice self-avoiding polygons in the bead-chain model. Using Clisby's tree data structure and the scale-free pivot algorithm, for each n between 10 and 27, we generated 243–n polygons of size 2*n*. Using a new knot diagram simplification and invariant-free knot classification code, we were able to determine the precise knot type of each polygon. The results show that the number of prime summands of knot type K in a random n-gon is very well described by a Poisson distribution. We estimate the characteristic length of knotting as 656,500 ± 2500. We also make new calculations for knotting rates and amplitude ratios of knot probabilities. We find that our calculations agree quite well with previous on-lattice computations. Our results support the idea of knot localization and the knot entropy conjecture.
, , # Data and code from: Random knotting in very long off-lattice self-avoiding polygons

Dataset DOI: [10.5061/dryad.zpc866tnv](https://doi.org/10.5061/dryad.zpc866tnv)

## Description of the data and file structure

Files are stored in plain text formats.

### Files and variables

#### mean_number_of_summands_and_tv_distance_to_poisson.tsv

This tab-separated file contains computed values of *λ~K~(n)*, our estimate of the expected number of factors of knot type *K* in a random self-avoiding *n*-gon, together with standard errors and total variation (TV) distance from the empirical distribution to the Poisson distribution with the same mean.

#### <K>_observed_summands.tsv

These tab-separated files contain observation data for the number of *N*-gons with *m* summands of knot type *K*. In each file, the first entry of each row is *N*, and the remaining entries list the various observed *m*'s and the number of polygons with that many factors of *K*.

For example, the file `5_2_observed_sum...,

本研究针对珠链模型中的非格点自回避多边形（off-lattice self-avoiding polygons）打结现象，报告相关实验结果。我们采用Clisby树数据结构与无标度枢轴算法，针对10至27区间内的每个n，生成了尺寸为2n的243–n个多边形。我们通过全新的纽结图简化与无不变量纽结分类代码，可精准确定每个多边形的纽结类型。研究结果显示，随机n边形中属于纽结类型K的素合成分支数目，可通过泊松分布（Poisson distribution）实现高精度拟合。我们估算得到打结特征长度为656500 ± 2500。我们还针对打结速率与纽结概率的振幅比开展了全新计算，结果表明本次计算结果与此前的格点计算结果吻合度良好。本研究结果为纽结定域化假说与纽结熵猜想提供了实证支撑。

数据与代码来源：《超长非格点自回避多边形中的随机纽结》

数据集DOI：[10.5061/dryad.zpc866tnv](https://doi.org/10.5061/dryad.zpc866tnv)

### 数据与文件结构说明
所有文件均以纯文本格式存储。

#### 文件与变量说明
##### mean_number_of_summands_and_tv_distance_to_poisson.tsv
该制表符分隔文件包含λ_K(n)的计算值——即随机自回避n边形中属于纽结类型K的合成分支数的期望估计值，同时附带标准误与经验分布相对于同均值泊松分布的总变差（total variation, TV）距离。

##### <K>_observed_summands.tsv
此类制表符分隔文件存储了含有m个纽结类型K合成分支的N边形的观测数据。每个文件的每行首项为N，其余条目依次列出各类观测得到的m值，以及对应具有该数量K合成分支的多边形数目。例如，文件`5_2_observed_sum...,`