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The tags on convexity are ($\times$560), ($\times$ 266), ($\times$ 420). Here the number is the current (2019/02/23) number of uses and I ignore some more specific tags whose meaning is quite well-identified such as or .

The tag currently (2019/02/23) has the usage guidance: A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ... Also, and have no usage guidance at this date.

Vaguely:

How could this be improved?

Adding tag guidance would require to have a more precise idea how to distribute the roles of these tags. But I see no coherent way to do so.

I see two essential meanings for "convexity": convexity of functions (closer to convex analysis) and convexity of bodies (closer to convex geometry, which also encompasses convexity in metric spaces). The distinction is clear in a number of cases, but this is also well-intertwined since convex functions are usually defined on convex subsets, while convex sets can usually be defined as sub-level sets of convex functions.

At this moment, a quick look at the actual use of seems to be a slight majority of questions on convex functions, an a large minority of convex geometry questions, and it's regularly used in combination with one of the other two tags (40%? I made no serious count).

At this point I see among the various options:

  1. Keep these 3 tags. I guess this considers that is the union of and . Improve usage guidance accordingly (how?) to avoid a too random use. Clarify when should be used: when both others are applicable? when at least one is applicable?
  2. Deprecate and use the two others (one or both).
  3. Make both and synonyms of , considering that the difference is not significant enough and that a broader tag would benefit.

Others options are welcome. The only thing I'm convinced is that statu quo is not a good option.


Edit: (to take into account Martin Sleziak's comment)

Here is a 2017/09/27 comment by François G. Dorais♦ about this issue:

" is perplexing since it's almost a meta-tag. My preference would be to have these questions remapped to , , and similar. However, this seems very implausible at the moment."

The closest option above is the technically easy (2), solving the issue for future questions. If one wants to solve the issue for past questions, if one wants to completely delete , one could imagine (if technically doable): remove from every question with at least one of the other 2 tags; for those tagged and none of the other 2, remove and add the other two (this will block for a few remaining ones for which there are already 5 tags but one can imagine these few can be dealt manually). But this can sound arbitrary, so just deprecating sounds enough, while users can then progressively manually delete past occurrences of deprecated .

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    $\begingroup$ I suppose you saw a comment by François G. Dorais♦ regarding this issue in the "Help improve tagging!" thread. I hope he will join into this discussion - he is the moderator who most frequently deals with tag-related issues. $\endgroup$ – Martin Sleziak Feb 24 at 19:38
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    $\begingroup$ It's pretty clear that convexity should disappear and needs to be deprecated; this will happen soon regardless. That said, convexity is a very complicated case and I am looking forward to what comes out of this discussion. YCor, if you don't mind, I can add a few comments to your post (clearly labeled as from me) to help guide the discussion. $\endgroup$ – François G. Dorais Feb 25 at 2:38
  • $\begingroup$ @FrançoisG.Dorais When you mention deprecating (convexity) in your comment, do you mean simply adding into the tag-excerpt that it is deprecated (similarly as for some other tags in the past), or also blacklisting the tag - which would prevent it from being used in the new questions? See also: The existing deprecated tags should be blacklisted. $\endgroup$ – Martin Sleziak Feb 25 at 5:27
  • $\begingroup$ @MartinSleziak The tag-excerpt option only. Blacklisting is mostly useful for repeat offenders: deprecated tags that get created over and over again. That problem is very rare on MO. $\endgroup$ – François G. Dorais Feb 25 at 6:04
  • $\begingroup$ @FrançoisG.Dorais sure, go ahead $\endgroup$ – YCor Feb 25 at 7:54
  • $\begingroup$ Could we maybe make "convex-polytopes" a synonym for "polytopes"? $\endgroup$ – Sam Hopkins Feb 27 at 20:05
  • $\begingroup$ Or I guess considering the number of things tagged with each tag, maybe the other way around? $\endgroup$ – Sam Hopkins Feb 27 at 20:06
  • $\begingroup$ @SamHopkins it deserves a specific discussion, could you make it a question at meta.mathoverflow.net/questions/862/help-cleanup-tags ? $\endgroup$ – YCor Feb 27 at 20:22
  • $\begingroup$ Sam's question is now there: meta.mathoverflow.net/a/4141/14094 $\endgroup$ – YCor Feb 27 at 20:31
  • $\begingroup$ @FrançoisG.Dorais This is related closer to deprecated tags in general rather than to this specific instance - so rather than continuing here in comments, I left a bit more on this issue here: Blacklisting (deprecated) tag while they still exist. (Although I suppose that to some extent I am mostly repeating the things from the older post on meta.) $\endgroup$ – Martin Sleziak Mar 2 at 6:15
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To go forth, here's one single suggestion, namely an expanded version of (2) in my question, namely do the following three things:

a) : its current tag guidance (which can be amended anyway, as any tag) is: "A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...". Add "Can be used in combination with related tags such as , , etc".

b) Add a tag guidance to . Here's a suggestion (which can be improved now or afterwards): "Convex functions, analysis on convex sets. Can be used in combination with related tags such as , , , etc."

c) Deprecate . Namely, change its (currently empty) tag guidance to "Deprecated: do not use this tag. Instead, use , , or related tags".

All this is easy to do, so if we agree let's go, and we can discuss afterwards about past posts tagged .

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