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currently has 13 questions bearing this tag. Should and be merged, or one be made a synonym of the other?

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    $\begingroup$ Except for the question about nomenclature of counting numbers, all the other (counting) questions seem to belong in (combinatorics). $\endgroup$ – Arturo Magidin Dec 11 '10 at 2:52
  • $\begingroup$ then should we just retag the questions? $\endgroup$ – Sean Tilson Dec 11 '10 at 3:33
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    $\begingroup$ Not sure. [counting] + [combinatorics] lets you know the kind of question to expect, while just [combinatorics] might not. Of course, once the question is read, but... $\endgroup$ – Aryabhata Dec 11 '10 at 5:07
  • $\begingroup$ @J.M.: If two tags are merged, can they be unmerged? Since users with more than rep $N$ for some $N$ (i don't remember) can create tags, what happens to merged tags that get "recreated". Or perhaps I am misunderstanding what merging means. $\endgroup$ – Timothy Wagner Dec 11 '10 at 15:34
  • $\begingroup$ As I understand it, mere retagging won't preclude the tag being used again by future questions. Turning, say [counting], into a [combinatorics] synonym would ensure that when future questions are tagged [counting], the system automagically retags them as [combinatorics]. I was about to retag one question, but since I do not think myself possessing combinatorics expertise, I am now asking here in meta. $\endgroup$ – J. M. is a poor mathematician Dec 11 '10 at 15:40
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    $\begingroup$ @Arturo: The fact that all [counting] questions belong in [combinatorics] just tells you that counting (i.e. enumerative combinatorics) is a subset of all combinatorics. In that respect, having both tags around seems no different than having both an [algebraic-topology] tag and a [topology] tag. Moreover, it's also worth having the tag around since a questioner might very well have a counting question without knowing what the word combinatorics means!! $\endgroup$ – Dan Petersen Dec 11 '10 at 21:08
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    $\begingroup$ @Dan Petersen: The question is whether there is sufficient demand for specific counting questions (or for more general combinatorics one) to justify having them separate; we don't have distinct tags for (finite-group-theory) and (group-theory), for instance. As for people with counting questions not knowing what combinatorics means, wouldn't making [counting] a synonym fix that? Someone who doesn't know the word would type "counting", and the system would automatically change it to [combinatorics]. $\endgroup$ – Arturo Magidin Dec 11 '10 at 21:10
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    $\begingroup$ Clarification re merging versus synonyms: merging is about existing questions; synonyms are about future questions. Merging [counting] into [combinatorics] would be a mass retagging of every [counting] question as [combinatorics] without bumping the questions to the top and with no effect on future questions. Setting [counting] as a synonym for [combinatorics] will cause any future use of [counting] to automatically be changed to [combinatorics] with no effect on existing questions. $\endgroup$ – Isaac Dec 11 '10 at 21:35
  • $\begingroup$ @Isaac: Thanks for that clarification. I would support making synonyms; I'm indifferent towards merging, but perhaps it would be a good idea if we go for synonymity. $\endgroup$ – Arturo Magidin Dec 12 '10 at 4:21
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My inclination is to make them synonyms, if that works as you describe (people who tag a question as "counting" simply get it automatically re-tagged). At least right now it doesn't seem like the counting vs. noncounting facets of combinatorics need separation here, though that could change in the future.

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I think my earlier comment was misunderstood. It does not currently seem clear that there is a reason to merge the tags or make them synonyms, at least not without someone with expertise saying this is reasonable. The point of my comment was that maybe we should retag the appropriate questions and not mess with the tags. Maybe there are people who know what combinatorics is and what counting is and mean counting, not combinatorics. Unless this impossible I see no reason to change the tags. Changing questions that are inappropriately tagged is something we will always have to do, and it isn't that big of a deal.

The point about AT and topology is a valid one, and until someone points out the harm of having multiple tags for things that are similar but not the same I think it wise to leave the tags unchanged.

At least 2 of the counting questions seem to be about counting and not combinatorics (maybe I am wrong, but the "why do our numbers start over..." and "what else can an elliptic integral count?" don't seem like combinatorics a priori.)

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