Posted Feb. 4, 2007.
>I think the results are new and the general plan is straightforward. It is not as straightforward as you think. You must have missed the subtle points. >It won't get the Fields medal Oh yea? Maybe you are right, but unless you happen to be Tim Gowers or Terry Tao, neither will any of your work get the Fields medal, and even though I don't know who you are (I very much doubt that you are either Tim Gowers or Terry Tao), I am willing to bet, that this paper is closer to Fields-quality work than any of your own papers. >but I don't think that's our criteria. How generous and gracious of you! >I do recommend it's acceptance. Thank so sooo much! You made my day. >Here are a few suggestions that would improve the paper. These suggestions would make it worse. >A. Include a few references to math books where Dyck paths are discussed. >Stanley's EC2, chapter 6 is the obvious choice. It would be good to mention >the connection with Catalan numbers and there is a paper of Krattenthaler >where the appearance of Chebyshev polynomials in such problems is treated >fully. Pretty irrelevant >B. The first 8 or so terms of the generating functions (41)-(49)should be >included along with EIS numbers. Pretty obsolete, nowadays, anyone can generate them himself or herself, and cut-and-paste it to Sloane (or even google) >C. If you take Dyck paths where all peaks are at height 2 you get the >Fibonacci numbers. Is there a similar result for the basketball case? Stupid comment that makes no sense.
Opinion 77 of Doron Zeilberger