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The paper I want to publish is just a conjecture.

  • 5
    put it on your blog and/or the arxiv – Artem Kaznatcheev Jul 10 '12 at 0:00
  • I removed the "publishers" tag, which seems irrelevant. – Benoît Kloeckner Jul 11 '12 at 8:57
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There are several ways in which conjectures propagate, and each has its own method for publishing.

  1. As future work/further direction on a set of theorems you proved. In this case, you submit the paper based on the set of theorems, and the conjecture is just a bonus. Your primary contribution is the original theorems.

  2. As a reasonable technical lemma to use to prove a difficult theorem. One again, submit as you would a paper proving any other theorem. Your primary contributions is the interesting/non-obvious consequence.

  3. As a consequence or expected result based on a novel model. In this case the empirical model is usualy motivated by some sort of science, attempt to publish in the relevant scientific or applied math journals. Your primary contribution is evidence in the reasonable model.

  4. As a synthesis of connections between many different areas of math that your conjecture brings together. Publish this as a survey that unifies the areas of interest. Your primary contribution is the connections between fields.

If your paper does not have any results apart from the conjecture, then such are usually disseminated informally. Tell your friends, colleagues, publish a blog post, ask for a proof on MO. This is a great way to find someone to work with in helping you turn your conjecture into a theorem.

  • 3
    To add one more example: As a general statement which unifies many more technical proven cases. You usually can't get into a top journal with this, but I have proven papers that prove "X is true for series-parallel matroids" and "X is true for transversal matroids" and "X is true for matroids of rank at most 3"... where the central theme of the paper is "Conjecture: X is true for all matroids". My advice here would be find a journal which would be interested in the truth of the conjecture, and aim a bit lower than if you had proved the full conjecture. – David E Speyer Jul 11 '12 at 15:00
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If your conjecture is supported by partial result, then as pointed out by Artem Kaznatcheev, a journal suited to this results is the good choice.

If it is supported by numerical computation, you can aim at "Experimental Mathematics".

If it is not supported, or supported only by previous results, then it would probably be difficult to publish. Sometimes conference proceedings can be a suitable place, but informal dissemination would probably be the most common practice.

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