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There are two tags: and which are both subsumed by the topic of combinatorics. I believe these should both be synonyms of . Perhaps permutations is debatable, because there may be some questions about which don't involve actually counting them, but I'm more confident that would be a good synonym candidate.

Any thoughts here?

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  • Out of 824 questions tagged , 135 questions are also tagged . That's one in six. I believe that group theory is not considered to be a subset of combinatorics.

  • In case of we only have 49 questions to look at. Seven of them are tagged either or . That's one in seven. While there is an overlap between combinatorics and probability in the form of probabilistic combinatorics, they remain distinct subjects. Although one could say that probability on a finite measure space is just counting, that would not be saying anything particularly smart.

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  • $\begingroup$ You are using both combinatorics and statistics and probability to draw conclusions. Isn't that a bit of begging the question? ;-) $\endgroup$
    – Asaf Karagila Mod
    Jul 20 '13 at 23:34
  • $\begingroup$ I'm disinclined to have the tags merged as OP suggests. Counting techniques are useful in many areas of math, not only combinatorics, and the latter, while making heavy use of counting techniques, is a "favorite" tag of mine to check for questions about combinatorial designs. $\endgroup$
    – hardmath
    Jul 21 '13 at 11:51
  • $\begingroup$ See also my comment above re:permutation+group-theory $\endgroup$ Jul 22 '13 at 7:53
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Edit: Thanks for the clarification. I didn't realize that "synonym" had a technical meaning on Stack Exchange sites. Here's a quote from your link:

A tag synonym is usually a tag that has exactly the same meaning as some other tag, such as and . In some cases, tags that are subsets of other tags will also be considered synonyms, such as for .

The system organizes tags in a master/synonym relationship. All uses of the synonym tag(s) for any given master tag are automatically converted to the master tag. So, users can enter a synonym tag when writing a question, but the master tag will be displayed when the question is loaded. Similarly, when users search for questions tagged with a synonym, a list of questions tagged with the master will be displayed.

Although tag synonyms are allowed to be subsets of the master tag, I would hope that people wouldn't regard as a large enough subset of for it to be appropriate to identify them. From my perspective, tagging basic combinations problems is like tagging basic derivative questions . But when I look at how most combinations questions are tagged on this site, they generally get the tag, not the tag, so my view is clearly a minority one.

Original answer: What do you mean by "synonym"? Are you saying that two of the three tags should be abolished, and only one kept? Or do you mean that the three tags should all be kept but should be considered interchangeable?

Certainly the field of combinatorics includes an immense amount of subject matter besides permutations and combinations, much of which has nothing to do with counting. On the other hand, permutations and combinations are taught in elementary courses in which the word "combinatorics" is most often never mentioned. Therefore it seems to me to be useful to have separate tags. And, as was mentioned in 40 votes' answer, permutations are important in noncombinatorial mathematics.

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  • $\begingroup$ meta.stackexchange.com/questions/70710/… $\endgroup$ Jul 21 '13 at 14:51
  • $\begingroup$ @Will, Thanks for the response in the other thread. I did not mean to withdraw the question by deleting my comment, but removed it only because the posting of a response made the question irrelevant and further discussion, if any, could have been about the statistics. It seems there is no disagreement on the bottom line, that even an over-correction for the effect you identified, would not invalidate the basic point of the answer (which was about A being comparable to B, C, et al, with no claim of superiority and actually a disclaimer of that, though A's uncorrected estimator was higher). $\endgroup$
    – zyx
    Dec 1 '13 at 23:15

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