[Math] Publishing conjectures

big-listjournalssoft-question

One has written a paper, the main contribution of which is a few conjectures. Several known theorems turned out to be special cases of the conjectures, however no new case of the conjectures was proven in the paper. In fact, no new theorem was proven in the paper.

The work was reported on a few seminars, and several experts found the conjectures interesting.

One would like to publish this paper in a refereed journal. The paper was rejected from a certain journal just two days after its submission because "this genre of article does not fit the journal".

QUESTION. Are there examples of publications of this genre in refereed journals?

ADD: The mentioned paper explains the background, states the conjectures, discusses various special cases and consequences, and lists known cases. It is 20 pages long.

Best Answer

If you have numerical evidence in support of the conjecture, the journal of Experimental Mathematics seems to fit the bill:

Experimental Mathematics publishes original papers featuring formal results inspired by experimentation, conjectures suggested by experiments, and data supporting significant hypotheses.

Note that we do value proofs: experimentally inspired results that can be proved are more desirable than conjectural ones. However, we do publish significant conjectures or explorations in the hope of inspiring other, perhaps better-equipped researchers to carry on the investigation. The objective of Experimental Mathematics is to play a role in the discovery of formal proofs, not to displace them.

Several publications in that journal have gotten quite some traction, like: