There are (r+1)(r+2)(2r+3)(r2+3r+5) Ways For the Four Teams of a World Cup Group to Each Have r Goals For and r Goals Against [Thanks to the Soccer Analog of Prop. 4.6.19 of Richard Stanley's (Classic!) EC1]

By
Shalosh B. Ekhad and Doron Zeilberger

.pdf   .ps   .tex  

First Written: July 7, 2014

[Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger and arxiv.org]


Dedicated to Richard Stanley (b. June 23, 1944), on his "number of ways for a simple Drunkard to return home after 8 steps"-th birthday

This short tribute to the guru of Enumerative and Algebraic Combinatorics started out when one of us (DZ) attended the Stanley@70 conference, that took place at the same time as the preliminary stage of the 2014 World Cup.


Maple Packages


Some Input and Output files for the Maple package GOALS


Some Input and Output files for the Maple package WorldCup


Personal Journal of Shalosh B. Ekhad and Doron Zeilberger

Doron Zeilberger's Home Page