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From my talk's slides, I have:

image of my talk slides, transcribed below

先结论...

对于给定m(即为确定的元素数量),m! #PLR(r,s,n;m)是个
- 三元多项式,
- 对称多项式(即#PLR(r,s,n;m)=#PLR(s,r,n;m)等),
- 整数系数的,
- 3m次多项式。

(I have some students here helping me debug this, but it's mostly my writing.)

I'm happy with the content, but I'm not comfortable with the grammar. I'm concerned about two things:

  1. A mismatch between 是个... and the third item 整数系数的 ("has integer coefficients"), but maybe this is okay.
  2. The lack of an "and" here (we would normally include it in English).

Question: In my bullet list, is ...是个... [something]的 problematic, and do I need an "and"?

  • Not so sure what's your question. Why not put them in one line, say 整系数的三次多项式. Besides, 先结论?It should be 先给出结论. 先结论 is unacceptable grammar. – user19549 Jul 9 '18 at 9:36
  • I intend to pause and discuss each item one by one. – Becky 李蓓 Jul 9 '18 at 9:41
  • Then say -整系数多项式 -3m次多项式. No "and". You're not actually making a sentence. You're using red arrow list symbols. – user19549 Jul 9 '18 at 9:43
  • I was just a little bit wondering that as in your another question you defined notation PLR(r,s,n;m) to be a subgraph but here obviously you r using operator # to calculate the cardinality, which means notation PLR(r,s,n;m) is the set of subgraphs with such properties. I don't know whether It's okay, or maybe you have considered this issue, then I am sorry for my question. – Toosky Hierot Jul 10 '18 at 1:21
  • PLR(r,s,n;m) is the set of partial Latin rectangles (a kind of combinatorial matrix), and each partial Latin rectangle has a correspondence with an m-vertex n-colored subgraph of K<sub>r</sub>□K<sub>s</sub> (which arises in the other question, looking at the right-hand side as a 3 by 4 matrix). To save notation, we also use PLR(r,s,n;m) as shorthand to refer to a member of PLR(r,s,n;m). And, yeah, I just add # in front to mean "the number of". [These are talk slides: So I aim to minimize text, and explain things verbally.] – Becky 李蓓 Jul 10 '18 at 1:57
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I have read the comments and reply, then I would like to give a demo in my way. We can discuss it.

首先给出结论 (This indicate that we will prove it in later slides...)

对于给定的m(即为确定的元素数量),多项式m! #PLR(r,s,n;m)具有以下特点:

  • 是三元多项式,
  • 是对称多项式(即#PLR(r,s,n;m)=#PLR(s,r,n;m)), (I'm just curious, what do you mean by 等 here? Does it mean #PLR(r,s,n;m)=#PLR(r,n,s;m) and so on?)
  • 是整数系数多项式,
  • 是3m次多项式。
  • (a) actually it was proved on previous slides, we prove more on subsequent slides (for which I need these intermediate conclusions); is this a problem? (b) I didn't want to write #PLR(r,s,n;m)=#PLR(s,r,n;m)=#PLR(n,r,s;m)=#PLR(r,n,s;m)=#PLR(s,n,r;m)=#PLR(n,s,r;m) in full, as it's a property of symmetric polynomials (称多项式) (c) I see I've left off a 的. – Becky 李蓓 Jul 9 '18 at 13:52
  • (a) OK, not a big problem. But we use 首先 or 先, sometimes it will indicate something will happen later... Anyway, it depends on context. (b) Make sense. (c) Still not a big problem, but just a little bit weird when I read this... – Bruce Huang Jul 9 '18 at 14:00
  • symmetric polynomials 对称多项式。“称多项式” means "It is named 多项式"。 – Bruce Huang Jul 9 '18 at 14:40
  • 具有如下特点 -> 具有如下性质 – tsh Jul 16 '18 at 2:10
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"先结论" is too much colloquial.And even in a colloquial situation,this expression is kind of confusing and impolite from my perspective though we will use it sometimes.

“是整系数多项式” or “是个整系数的多项式” 。 There is no such a structure as “是个……的” in the 普通话's grammer.

"and" is not necessary.

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I ve made great adjustments

先给结论:

对于元素数量m给定的情况,m!#PLR(r,s,n;m)具有如下性质:

  • 为r,s,n三元多项式,

  • 为关于r,s,n的对称多项式(即给r,s,n的任意排列依次替换原变量,多项式不变),

  • 为整系数多项式,

  • 为3m次多项式。

These changes are made according to my received tradition in math class.

  • Good. But I still insist on using "先给出结论". And "对于给定的元素数量m" sounds formal. – Bruce Huang Jul 11 '18 at 15:05

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