I'm a high school student. My peer and I have done some work on the Ballot Theorem counting problem and Catalan Numbers. We have come up with a new proof to the Ballot Theorem and we demonstrate the duality between the Ballot Theorem and Catalan Numbers. Or at least we hope the proof is new, we've scourged the net and not found work similar enough to ours. We'd like to send it a journal for a review process, and also try our shot at publishing. What are our chances at getting published, and which journal should we try in?
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14$\begingroup$ A minor non-mathematical correction: I think you mean you "scoured" the net, not "scourged" it $\endgroup$– Yemon ChoiCommented Jul 6, 2018 at 12:41
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4$\begingroup$ May be you can give an outline of what you have done here on MO.. Some one (experienced in publishing papers) who has same interest as you might respond... Then you can send her/him your paper for more detailed review... Once you (and the reviewer, not necessarily just one) thinks it is good enough you can then try sending it to some journal.. reviewer can suggest what is suitable.. $\endgroup$– Praphulla KoushikCommented Jul 6, 2018 at 13:15
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7$\begingroup$ Have you posted it on Arxiv? $\endgroup$– user102087Commented Jul 6, 2018 at 14:55
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1$\begingroup$ Mathematics Magazine. College Mathematics Journal. $\endgroup$– Gerry MyersonCommented Jul 6, 2018 at 23:35
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$\begingroup$ If you are unsuccessful with a professional journal, you could try the Rose-Hulman Undergraduate Mathematics Journal (scholar.rose-hulman.edu/rhumj). They say that the paper must be written by undergraduates, but perhaps they also allow high school students. $\endgroup$– Richard StanleyCommented Jul 7, 2018 at 2:06
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You may want to try Combinatorics, Probability & Computing or The Electronic Journal of Combinatorics. Your chances at getting published depend on the quality of your paper.