By Shalosh B. Ekhad
(Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger)
FirstWritten: June 13, 2016 This Version: July 26, 2016.
In his beautiful article, "An American Tournament Treated by the Calculus of Symmetric Functions" Quarterly J. of Pure and Applied Mathematics. vol. XLIX, No. 193, 1920, The combinatorial giant, (and amazing human calculator), Major Percy Alexander MacMahon, considered round-robin tournaments for n players for n from 2 to 9, and for each found all the possible score vectors, and determined the most popular one, as well as the number of times it shows up. In this article, we continue this work up to n= 15, and thereby continue OEIS sequence A274098.