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Over the past month, I have used (and perhaps abused) both MSE and MO in order to obtain certain purely mathematical information of critical importance to my team at this point in its research trajectory.

In the course of doing so, I have posted questions like this one at MSE:

Is there an internally consistent nearest-neighbor relation in this complete linearization of the 240 roots of $E_8$?

and this one at MO:

$E_6$, $E_8$, and Coxeter's (anti-)prismatic projections of the n-dimensional cross-polytopes

And in the course of discussion with folks who've commented on these questions, it became very obvious to me that folks who know $E_6$ and $E_8$ very well from an algebraic group-theoretic perspective do not know nearly as much about the two polytopes $1$$_2$$_2$ and $4$$_2$$_1$ which respectively instantiate the root systems of these two groups.

For example, see the information regarding the {84,72,84} decomposition of $4$$_2$$_1$ and the {21,30,21} decomposition of $1$$_2$$_2$ which I provided in my second answer to this question:

$E_6$, $E_8$, and Coxeter's (anti-)prismatic projections of the n-dimensional cross-polytopes

I would bet even money that few algebraic group specialists are familiar with these two polytope decompositions, and what they can tell us about the two corresponding groups.

And I would bet the same amount that few polytope specialists are familiar with the algebraic group-theoretic implications of these polytope decompositions.

So, here's my question: should MSE have a "distinguished" class of questions which can be tagged "cross-specialty", in order to alert people that a question requires consideration by more than one kind of specialist at MSE?

(I believe it is the case that most questions to MSE do NOT require the attention of more than one kind of specialist, though I may well be wrong about this.)

Edited 1/19/2018 to add:

For a similar case of a legitimately "cross-specialty" question, see this related question at metaMO:

https://meta.mathoverflow.net/questions/3597/how-would-you-tag-an-mo-question-involving-both-zumkeller-numbers-a083207-and

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    $\begingroup$ I think we should try, but attempts often clash with other norms we have developed over the years. I will collect my thoughts on this when I have a bit more time $\endgroup$ – Jyrki Lahtonen Jan 17 '18 at 12:08
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    $\begingroup$ You can give your questions up to five tags. You can tag your question algebraic-groups and also tag that same question polytopes and also tag it root-systems and also tag it cross-specialty and also tag it pain-in-the-butt, if you like. So what is the point of your question? $\endgroup$ – Gerry Myerson Jan 17 '18 at 17:40
  • $\begingroup$ @GerryMyerson - there is an actual tag "cross-specialty"? My apologies - I wasn't aware . . . but more to the point, I'm talking about a tag that would indicate that the question can probably not be answered by persons in just one specialty ... kind of like a "heads-up" to view the question differently than questiosn seem to be viewed around here. $\endgroup$ – David Halitsky Jan 17 '18 at 17:54
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    $\begingroup$ In my view, MSE is not an appropriate resource for long, ongoing research projects. It is a site for providing answers for focused, specific, answerable questions. It's not a matchmaking site for finding research collaborators; if you want to have a collaboration, do it directly with the people rather than running everything through MSE. In short, if a question requires work by multiple experts from different areas, it is (far) out of scope for MSE. $\endgroup$ – user296602 Jan 17 '18 at 19:12
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    $\begingroup$ Also, a much more limited comment: Tags should describe question content, not question style. There's a long history of meta-tags on MSE and there are a lot of good reasons that we tend to avoid them. The homework tag was burninated a long time ago, and other meta-tags have met similar fates. A "cross-specialty" tag would be in the same style, and I think it is not a good tag to have here. $\endgroup$ – user296602 Jan 17 '18 at 19:16
  • $\begingroup$ @user296602 - thanks as always for taking the time to respond. I can see your point from a "long-term" point of view, but why NOT some kind of short-term permitted functionality for initial "hook-up" of folks who may later collaborate (or consumnate, if you will ... LOL)? Kind of like a dating service, to use your analogy $\endgroup$ – David Halitsky Jan 17 '18 at 19:22
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    $\begingroup$ Math Stack Exchange is not a social networking site, and shouldn't be one. $\endgroup$ – user296602 Jan 17 '18 at 19:25
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    $\begingroup$ @user296602 - is that straw peeking out of the sleeve of that comment? LOL !!! I have seen you do a LOT better than that, and I've only been here less than two months .. . $\endgroup$ – David Halitsky Jan 17 '18 at 19:27
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    $\begingroup$ To add to @user296602's comment, here you can read about The “meta-tags”. (I have already mentioned that post to you in chat, but I guess it should also be mentioned here, since it is related to the discussion.) $\endgroup$ – Martin Sleziak Jan 17 '18 at 19:32
  • $\begingroup$ @MartinSleziak - yes - and I guess I'm saying that "cross-specialty" IS a good meta-tag for a certain kind of question that DOES have a specific answer - e.g. "Is such-a-such polytope decomposition ever used in such-and-such algebraic-group context" - to me that question is both specific and fully answerable, apart from doing a possible service to the community. (Unless it is a disservice to the community to ask anything but specialty-internal questions . . .) $\endgroup$ – David Halitsky Jan 17 '18 at 19:39
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    $\begingroup$ @DavidHalitsky "This question is related to multiple areas" is clearly communicated by using the tags from multiple areas. Adding an extra tag about that is just unnecessary noise that doesn't help to organize things. And the whole point of using tags is to organize questions nicely. $\endgroup$ – user296602 Jan 17 '18 at 19:42
  • $\begingroup$ @user296602 - here's why I think you're not 100% correct, though you are surely partially correct in certain cases. I think that sometimes multiple specialty tags can and should be used when folks think that an answer CAN be provided in only one of the tagged specialities, but they're not sure which. That is very different from the kind of case I'm talking about here. $\endgroup$ – David Halitsky Jan 17 '18 at 19:47
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    $\begingroup$ Once you have the requisite number of points, David, you can tag your questions whatever you like. Of course, tags, like everything else here, are under the scrutiny of the users and/or moderators, so they may get destroyed soon after they're created, if they rub enough of the right people the wrong way. $\endgroup$ – Gerry Myerson Jan 18 '18 at 5:37
  • $\begingroup$ @GerryMyerson - thanks, GM - I'll keep that in mind 6 months down the road, assuming my first probationary question doesn't put me back under a ban at that point . . . $\endgroup$ – David Halitsky Jan 18 '18 at 5:48
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    $\begingroup$ @user296602 And I also strongly disagree with your claim that this site is for focused specific questions. I very much prefer a vague question, asked using self-made idiosyncratic notation by a retiree intrigued by the motion of his paint mixer to the type of "focused, narrowly defined" question copy/pasted from a homework sheet but with the appropriate amount of "context" included to make it passable to local guardians of quality. The latter only induce several posts of worthless five-minute-math that somebody who thinks they are sitting in an exam can produce by turning a crank. $\endgroup$ – Jyrki Lahtonen Jan 20 '18 at 0:16
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If you look at my interchange with user296602 in the comments on this question, you will see that a very interesting distinction arose between two different possible reasons for a member's use of multiple speciality tags on a question:

1) the member thinks that the answer can be provided by someone in just ONE specialty, but the member is not sure which one (one can easily see this happening if the question seems potentially answerable by a specialist in "algebraic-groups", or a specialist in "Lie-groups", or a specialist in "Coxeter-groups".)

2) the member thinks that the answer CANNOT be provided by someone in just one specialty, because a correct answer requires deep knowledge from specialists in at least two different specialties (for example, "polytopes" and "algebraic groups".)

I believe it is both fair and correct to say that reason (2) is a justifiable reason for use of a specific "cross-specialty" tag, and reason (1) is NOT.

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  • $\begingroup$ To a significant degree I disagree. I don't think your questions would benefit from a new cross-specialty tag. For example, an expert on algebraic groups or Lie groups is necessarily very well informed about root systems as well as Coxeter groups. OTOH they may not know much about polytopes. Also the structure you have described don't seem to have anything at all to do with either Lie groups or algebraic groups. At least so far it has been only about root systems and their Weyl groups. $\endgroup$ – Jyrki Lahtonen Jan 20 '18 at 0:30
  • $\begingroup$ IMHO you could get better answers, better reception from other users, and better results with questions of the type: Here is a list of tricodons that we think can be brought under a common umbrella using their group of symmetries. What symmetries does this set have? My guess is that such questions would be more fruitful. $\endgroup$ – Jyrki Lahtonen Jan 20 '18 at 0:36
  • $\begingroup$ You see, when Lie theory was used in particle physics (they were handing out Nobel prizes for that stuff in the 60's), they went about it approximately as follows. The observed elementary particles seemed to fit into patterns. Those patterns came from representations of certain Lie groups. But that was a 2-way street! The group theory was used to predict the existence of previously unknown particles. Also the groups could be used to model the behavior of those particles (e.g. describe the kind of reactions they could take part in). $\endgroup$ – Jyrki Lahtonen Jan 20 '18 at 0:42
  • $\begingroup$ But, those physicists didn't start by fixing the group. They let their observations lead the way in the choice of the group. Is there anything like this you want to achieve here? What do you plan to do with the symmetry group when/if you find it? Predict some previously unknown tricodons? Classify them in a simpler way? Whatever it is, it sounds more likely that you also need the observations and symmetry properties of the tricodons lead the way. They define the group, and the algebra people here will happily assist you in identifying the group. $\endgroup$ – Jyrki Lahtonen Jan 20 '18 at 0:48
  • $\begingroup$ But, for some reason you seem to be sold on the idea that the group of symmetries must be related to the symmetries of $E_8$ lattice. May be because your set has exactly 240 objects? That's a tip, sure, but a collection of 240 objects can have a huge variety of symmetry groups. It could be the huge group of all permutations of those 240 object (there are approximately $4\cdot 10^{468}$ of those. It could be the Weyl group of type $E_8$ with $696729600$ elements. It could be something much smaller. $\endgroup$ – Jyrki Lahtonen Jan 20 '18 at 0:55
  • $\begingroup$ What has been baffling me all this time is, why $E_8$. Why a group generated by eight reflections? This has lead to, pardon me, something that look like exercises in numerology desperately trying to fit the collection to a predetermined group as opposed to letting the tricodons tell us what the group is. $\endgroup$ – Jyrki Lahtonen Jan 20 '18 at 0:58
  • $\begingroup$ Of course, it is highly likely that I'm totally wrong about what your project needs. Sorry if I wasted your time airing my misgivings. I guess the point is that I would need to keep an open mind about how the symmetries can be used (that would fall on your side of the court), and you would need to keep an open mind about which group it is :-) $\endgroup$ – Jyrki Lahtonen Jan 20 '18 at 1:06
  • $\begingroup$ @JyrkiLahtonen - if my team ONLY had a list of 240 objects, I would of course agree that ALL your concerns and suspicions are well-justified. We now in fact have a triple of numbers 176,240,336 with demonstrably deep relations to the way in which the 72 $E_6$ roots co-locate with 72 of the 240 $E_8$ roots, and in addition, we think we may understand why this triple is not only showing up as three Zumkeller numbers in A083207, but also (when divided thru by 16) as the numbers 11,15,21 in A152682. (certain labels for which edge-magic injections exist.) (Continued next comment) $\endgroup$ – David Halitsky Jan 20 '18 at 1:23
  • $\begingroup$ @JyrkiLahtonen - but this is obviously not the place to show you everthing that's going on. If you have the time and interest, send me an email at halitsky@att.net, and I will send you a brief write-up that I'm presently preparing in the hope that TD Noe will kindly look at it (primepuzzles.net/thepuzzlers/Noe.htm) And thanks again for the time you're spending on this matter . . . $\endgroup$ – David Halitsky Jan 20 '18 at 1:26
  • $\begingroup$ Another link to TD Noe: oeis.org/wiki/User:T._D._Noe . . . $\endgroup$ – David Halitsky Jan 20 '18 at 1:33
  • $\begingroup$ @JyrkiLahtonen - TD Noe has graciously and kindly agreed to review my write-up on how we got to 240, and more generally, the Zumkeller numbers (176,240,336) and the edge-magic injection label numbers (11,15,21). Here is a link to a PDF of the write-up at DropBox. It should convey ALL the relevant biomolecular patterns which you have asked to see. dropbox.com/s/7rtt0iqmgimsgzu/Zumkeller_edge-magic.pdf?dl=0 $\endgroup$ – David Halitsky Jan 21 '18 at 20:34
  • $\begingroup$ @JyrkiLahtonen - see also the paper by Balmurugan et al (2016) which I have placed at DropBox here: dropbox.com/s/lmucri4kkutrroa/… After a member of my team reviwed the write-up for Noe which I provided in my last comment, he responded with the following comment: "It appears Zumkeller numbers can be used to label full binary trees such as decision trees . . . One corollary of the Balamurugan et al. study is that ‘Every binary tree admits a Zumkeller labeling’ of the graph." $\endgroup$ – David Halitsky Jan 22 '18 at 3:48
  • $\begingroup$ @JyrkiLahtonen - I am pleased to tell you that Egon Schulte is kindly giving me some office time next week in Boston. Among other matters, we will be disussing this progression (which of course arises from our biomolecular data): I )16 5-cells (pentachorons or pentatopes) and 16 2_21's; II) 8 8-cells (octachorons or tesseracts) and 8 3_21's; III) 2 16-cells (hexadekachorons or 4-orthoplexes) and 2 4_21's. I mention this to show you that I am taking your advice and keeping an open mind about what the relevant mathematical structures might be (apart from $E_8$). $\endgroup$ – David Halitsky Jan 25 '18 at 3:11

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