On the Most Commonly-Occurring Score Vectors of American Tournaments of n-players, and their Corresponding Records

On the Most Commonly-Occuring Score Vectors of American Tournaments of n-players, and their Corresponding Records
By Shalosh B. Ekhad
article(.txt)

(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.

Maple Packages

PERCY.txt

PERCYG.txt (a generalized version of the above

Sample Input and Output Files for the Maple package PERCY.txt

This article was produced by running the
input file, yielding output file (i.e. the above article).

This took quite a while, but in 9 seconds, we get 12 terms:
input file, yielding output file

It only takes 0.1 seconds to reprdouce Macmahon's original values, up to n=9
input file, yielding output file

Sample Input and Output Files for the Maple package PERCYG.txt

To get a more detailed article, in the style of MacMahon
input file, yields output file

To get the Chess analog
input file, yields output file

To get the Soccer analog
input file, yields output file

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