<p>I am absolutely not a mathematician, but here is my stab:</p>

<p>isotropic: "having the same properties in all directions,"</p>

<p>In your case, a regular matrix, your example showing the vertical and horizontal elements to be the same.</p>

<p>合痕：isotropy<br>
合痕类：isotropic<br>
合痕类的个数： isotropic elements / individual elements<br>
矩阵: matrix</p>

<p>本文继续讨论n=4的情形，<br>
This document goes on to discuss n=4 matrices<br>
给出了(4,k,1)-拉丁阵，(4,2),(4,3)-和<br>
showing (4,k,1) - Latin matrices, (4,2), (4,3)- and<br>
(4,4)-拉丁阵及它们的合痕类的个数。<br>
4 by 4 Latin matrices and their isotropic elements</p>

CC BY-SA 4.0
2018-06-03T23:23:31.963Z
Thanks!  (It's going to be "isotopic" rather than "isotropic", but I get the point.)  So it looks like 个数 is used to mean "representative" (one from each isotopy class).
Becky 李蓓
CC BY-SA 4.0
2018-06-04T01:44:52.133Z
bkrs: isotropy; isotropism **各向同性** (一物质在各方向具有相同物理性质的特性),also **各项同性**  examples from iciba: .在这儿,我们给出适用于各项同性固体的方程.为了简单起见,仅讨论各向同性材料.re 合痕 also see baidu: 嵌入合痕 isotopy of embeddings，Q mentioned the term "trace" as supplied by google, users note that the mathematical term "trace" agrees with the general term 迹(繁体：跡) (see Wikipedia,e.g.)
user6065
CC BY-SA 4.0
2018-06-04T03:43:34.603Z
'isotope' is a word first used in 1913, suggested by the Scottish writer and doctor Margaret Todd from the Greek 'iso' = equal, same, 'topos' = place. The idea is, different atoms of the same element may have different atomic weights, but they are still 'in the same place in the periodic table'. To my mind, this clearly belongs to the field of chemistry. If mathematicians have commandeered the word and somehow applied it to maths, I would not know. My definition of isotopy would be: the phenomenon of having isotopes. It may be easy to confound isotopy and isotropy.
Pedroski
CC BY-SA 4.0
2018-06-03T22:52:34.390Z
2018-06-03T22:52:34.390Z
Pedroski
<p>From the mathematics article <a href="http://xueshu.baidu.com/s?wd=paperuri%3A%282e7daf094bbceef55b93de6d770de971%29&amp;filter=sc_long_sign&amp;sc_ks_para=q%3D%E6%8B%89%E4%B8%81%E9%98%B5%E7%9A%84%E6%9E%9A%E4%B8%BE%E5%92%8C%E8%AE%A1%E6%95%B0%28%E2%85%A1%29%3A%E6%83%85%E5%BD%A2n%3D4%2Ck%E3%80%88%3D4&amp;sc_us=16090247759279202218&amp;tn=SE_baiduxueshu_c1gjeupa&amp;ie=utf-8" rel="nofollow noreferrer">拉丁阵的枚举和计数(Ⅱ):情形n=4,k〈=4</a>, we have the following first paragraph:</p>

<p><a href="https://i.sstatic.net/aJoi2.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/aJoi2.png" alt="snippet from the paper"></a></p>

<p>I'm confused about what 合痕类的个数 (hé hén lèi de gè shù) means here (it's used twice).  <a href="https://translate.google.cn/#zh-CN/en/%E5%90%88%E7%97%95%E7%B1%BB%E7%9A%84%E4%B8%AA%E6%95%B0" rel="nofollow noreferrer">Google Translate</a> says it means "the number of traces", but I don't feel this is accurate.</p>

<p><strong>Question</strong>: What does 合痕类的个数 (hé hén lèi de gè shù) mean in this mathematics article?</p>

<p>My transcription: </p>

<blockquote>
  <p>文献[1]中引人了(n,k)-拉丁阵概念，并对n=2，3的情形给出了(n,k)-拉丁阵和它们的<strong>合痕类的个数</strong>。本文继续讨论n=4的情形，给出了(4,k,1)-拉丁阵，(4,2),(4,3)-和(4,4)-拉丁阵及它们的<strong>合痕类的个数</strong>。</p>
</blockquote>

<p>My translation:</p>

<blockquote>
  <p>In document [1] is the fascinating<sup>引人 (short for <a href="http://www.xiaoma.info/compound.php?cp=%E5%BC%95%E4%BA%BA%E5%85%A5%E8%83%9C" rel="nofollow noreferrer">引人入胜</a> (?))</sup> concept<sup><a href="http://dict.cn/%E6%A6%82%E5%BF%B5" rel="nofollow noreferrer">概念</a></sup> of the (n,k)-Latin matrix, and the case<sup><a href="http://dict.cn/%E6%83%85%E5%BD%A2" rel="nofollow noreferrer">情形</a></sup> of n=2,3, gives (n,k)-Latin matrices and their [合痕类的个数 (?)].  In this paper, we continue<sup><a href="http://dict.cn/%E7%BB%A7%E7%BB%AD" rel="nofollow noreferrer">继续</a></sup> the discussion<sup><a href="http://dict.cn/%E8%AE%A8%E8%AE%BA" rel="nofollow noreferrer">讨论</a></sup> to the case<sup><a href="http://dict.cn/%E6%83%85%E5%BD%A2" rel="nofollow noreferrer">情形</a></sup> of n=4, give (4,k,1)-Latin matrices, (4,2), (4,3), and (4,4)-Latin matrices and their [合痕类的个数 (?)].</p>
</blockquote>

<p>If it helps, here's an example of what one looks like:</p>

<p><a href="https://i.sstatic.net/WEfGK.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/WEfGK.png" alt="enter image description here"></a></p>

CC BY-SA 4.0
2018-06-03T05:01:43.633Z
search web for 合痕类, get e.g. 2001
 
Journal of Beijing University of Posts and Telecommunications
Vol. 24 No. 1
文章编号
: 1007-5321(2001) 01-0028-04
拉丁方合痕分类的快速算法
  
An Efficient Algorithm of Latin Squares Isotopy Classfication

合痕 isotopy 合痕类 isotopy class, also bkrs 合痕 isotopy,合痕分类(的算法) isotopy classification
user6065
<meaning-in-context>
What does 合痕类的个数 (hé hén lèi de gè shù) mean in this mathematics article?
# What does 合痕类的个数 (hé hén lèi de gè shù) mean in this mathematics article?

(Asked by: username_0 on 2018-06-03)

From the mathematics article [拉丁阵的枚举和计数(Ⅱ):情形n=4,k〈=4](http://xueshu.baidu.com/s?wd=paperuri%3A%282e7daf094bbceef55b93de6d770de971%29&filter=sc_long_sign&sc_ks_para=q%3D%E6%8B%89%E4%B8%81%E9%98%B5%E7%9A%84%E6%9E%9A%E4%B8%BE%E5%92%8C%E8%AE%A1%E6%95%B0%28%E2%85%A1%29%3A%E6%83%85%E5%BD%A2n%3D4%2Ck%E3%80%88%3D4&sc_us=16090247759279202218&tn=SE_baiduxueshu_c1gjeupa&ie=utf-8), we have the following first paragraph:

[![snippet from the paper](https://i.sstatic.net/aJoi2.png)](https://i.sstatic.net/aJoi2.png)

I'm confused about what 合痕类的个数 (hé hén lèi de gè shù) means here (it's used twice). [Google Translate](https://translate.google.cn/#zh-CN/en/%E5%90%88%E7%97%95%E7%B1%BB%E7%9A%84%E4%B8%AA%E6%95%B0) says it means "the number of traces", but I don't feel this is accurate.

**Question**: What does 合痕类的个数 (hé hén lèi de gè shù) mean in this mathematics article?

My transcription:

> 文献[1]中引人了(n,k)-拉丁阵概念，并对n=2，3的情形给出了(n,k)-拉丁阵和它们的**合痕类的个数**。本文继续讨论n=4的情形，给出了(4,k,1)-拉丁阵，(4,2),(4,3)-和(4,4)-拉丁阵及它们的**合痕类的个数**。

My translation:

> In document [1] is the fascinating引人 (short for [引人入胜](http://www.xiaoma.info/compound.php?cp=%E5%BC%95%E4%BA%BA%E5%85%A5%E8%83%9C) (?)) concept[概念](http://dict.cn/%E6%A6%82%E5%BF%B5) of the (n,k)-Latin matrix, and the case[情形](http://dict.cn/%E6%83%85%E5%BD%A2) of n=2,3, gives (n,k)-Latin matrices and their [合痕类的个数 (?)]. In this paper, we continue[继续](http://dict.cn/%E7%BB%A7%E7%BB%AD) the discussion[讨论](http://dict.cn/%E8%AE%A8%E8%AE%BA) to the case[情形](http://dict.cn/%E6%83%85%E5%BD%A2) of n=4, give (4,k,1)-Latin matrices, (4,2), (4,3), and (4,4)-Latin matrices and their [合痕类的个数 (?)].

If it helps, here's an example of what one looks like:

[![enter image description here](https://i.sstatic.net/WEfGK.png)](https://i.sstatic.net/WEfGK.png)

**Tags:** meaning-in-context
> **Comments:**
> **username_1**: search web for 合痕类, get e.g. 2001   Journal of Beijing University of Posts and Telecommunications Vol. 24 No. 1 文章编号 : 1007-5321(2001) 01-0028-04 拉丁方合痕分类的快速算法    An Efficient Algorithm of Latin Squares Isotopy Classfication  合痕 isotopy 合痕类 isotopy class, also bkrs 合痕 isotopy,合痕分类(的算法) isotopy classification  

---

## 1 answers

### Answer by username_2 on 2018-06-03. Score: 1 | Accepted answer

I am absolutely not a mathematician, but here is my stab:

isotropic: "having the same properties in all directions,"

In your case, a regular matrix, your example showing the vertical and horizontal elements to be the same.

合痕：isotropy  
合痕类：isotropic  
合痕类的个数： isotropic elements / individual elements  
矩阵: matrix

本文继续讨论n=4的情形，  
This document goes on to discuss n=4 matrices  
给出了(4,k,1)-拉丁阵，(4,2),(4,3)-和  
showing (4,k,1) - Latin matrices, (4,2), (4,3)- and  
(4,4)-拉丁阵及它们的合痕类的个数。  
4 by 4 Latin matrices and their isotropic elements

> **Comments:**
> **username_0**: Thanks!  (It's going to be "isotopic" rather than "isotropic", but I get the point.)  So it looks like 个数 is used to mean "representative" (one from each isotopy class).  
> **username_1**: bkrs: isotropy; isotropism **各向同性** (一物质在各方向具有相同物理性质的特性),also **各项同性**  examples from iciba: .在这儿,我们给出适用于各项同性固体的方程.为了简单起见,仅讨论各向同性材料.re 合痕 also see baidu: 嵌入合痕 isotopy of embeddings，Q mentioned the term "trace" as supplied by google, users note that the mathematical term "trace" agrees with the general term 迹(繁体：跡) (see Wikipedia,e.g.)  
> **username_2**: 'isotope' is a word first used in 1913, suggested by the Scottish writer and doctor Margaret Todd from the Greek 'iso' = equal, same, 'topos' = place. The idea is, different atoms of the same element may have different atomic weights, but they are still 'in the same place in the periodic table'. To my mind, this clearly belongs to the field of chemistry. If mathematicians have commandeered the word and somehow applied it to maths, I would not know. My definition of isotopy would be: the phenomenon of having isotopes. It may be easy to confound isotopy and isotropy.  

---

