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Suppose that the classification of some mathematical (say algebraic) notions requires (say) 70 pages. Let clarify that (say) 90% of the pages are used to write the result itself, whereas only 10% are required to introduce the notions, to mention some theorems and to explain the computer programs used. Finally, assume that the data of this classification is useful to some (pure) mathematicians, and also to some physicists (like an atlas).

Question: Where to published such a classification? (refereed) book or journal? Where?

The classification I have in mind: multiplicity-free complex fusion categories up to rank $6$, and braiding structures.

Sebastien Palcoux
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    Hard to say without more specifics about the significance of the result, but it's worth noting that there are many online journals which essentially don't have page limits. Of course getting someone to agree to referee a paper like this might be difficult... – Sam Hopkins Mar 10 '21 at 18:10
  • Some more specificity might help: you say "say algebraic", but is that actually the situation you have in mind, or just an example? In fact, why not say exactly what you are classifying, for most precision? Which journals accept very long technical papers very much depends on their subject. (EDIT: Turns out I just said what @SamHopkins was quicker to say. :-) ) – LSpice Mar 10 '21 at 18:10
  • This seems like a situation where the paper should include/point to the computer code used to generate the classification. It seems like the referees job would mainly be to verify the code. – user1504 Mar 10 '21 at 18:36
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    For a project of this type I would say that the result of the classification (and not just the code behind it) should also be primarily presented in machine-digestible form, preferably with a choice of formats and a convenient interface for searching etc. A 60 page list of cases in PDF form is not very useful. – Neil Strickland Mar 10 '21 at 20:53
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    @NeilStrickland: yes, all the data will be available in this webpage: http://www.thphys.nuim.ie/AnyonWiki/index.php/Main_Page But what about peer-reviewing? – Sebastien Palcoux Mar 10 '21 at 21:00
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    I am not sure, but since this is apparently not a complete classification, maybe a dynamic survey in the electronic journal of combinatorics would fit. – Martin Rubey Mar 10 '21 at 21:27
  • @MartinRubey: why are you saying that it is apparently not a complete classification? It is complete up to rank 6. A classification for all ranks may be unreachable. – Sebastien Palcoux Mar 10 '21 at 21:30
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    Possibly "Mathematics of Computation" would be appropriate if the classification is computationally heavy. – JoshuaZ Mar 11 '21 at 00:01
  • The Atlas of Lie Groups is an example of such a project. What have they done? – Alexander Woo Mar 11 '21 at 03:25
  • @AlexanderWoo: they wrote a book: https://en.wikipedia.org/wiki/ATLAS_of_Finite_Groups which now is updated as en electronic database : http://brauer.maths.qmul.ac.uk/Atlas/v3/ – Sebastien Palcoux Mar 11 '21 at 11:17
  • @SebastienPalcoux I thought it might be conceivable that the classification could be extended some day. I know nothing about fusion categories, so I don't know whether rank 7 would make sense at all. I was just thinking about the Ramsey number survey. – Martin Rubey Mar 11 '21 at 12:48
  • @MartinRubey: Yes, it makes sense for every rank. Your suggestion of journal is interesting, I did not know the concept of dynamic survey. The classification at rank 7, 8 or even 9 is a project, but it will requires a huge amont of extra works (both theoretical and computational). But it may be unclassifiable for all rank (that contains all finite groups, and much more). – Sebastien Palcoux Mar 11 '21 at 14:25
  • @SebastienPalcoux - That's a different project! (Lie \neq finite). But you've pointed to another good example. – Alexander Woo Mar 11 '21 at 17:21

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Perhaps I can try a suggestion: a journal which accepts long papers on the topics you sketched, aimed towards pure and applied mathematicians (including physicists and engineers), which has also an illustrious history is the Journal published by Castelnuovo Institute of Mathematics of the Sapienza University of Rome, i. e. the "Rendiconti di Matematica e delle sue Applicazioni". On the homepage of the Journal, you can read the following statements:

The Journal "Rendiconti di Matematica e delle sue Applicazioni" is regularly issued since 1914. The Journal traditionally publishes high-quality research articles in Pure and Applied Mathematics and adheres to the EMS Code of Practice.

Articles of any length are considered for publication. Submission of surveys, of articles of foundational nature, of doctoral dissertations etc. is also encouraged. Every article submitted is subjected to a first screening by the Editorial board: if the manuscript meets the journal’s basic requirements, it will be sent to a referee for a single blind peer review process. Once a paper is accepted it goes immediately into production and published online shortly after the approval of galley proofs.

I am almost sure that the impact factor of the journal is not "between the top ones": however in the past it has published several important papers and many illustrious mathematicians have been its directors (Volterra, Severi, Segre, Fichera, to cite a few names). Well, my two cents.

Daniele Tampieri
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