There are $(r+1)(r+2)(2r+3)(r^2+3r+5)$ 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]

Doron Zeilberger; Shalosh B. Ekhad

arxiv: 1407.1919 · v1 · pith:NFWDCNVXnew · submitted 2014-07-08 · 🧮 math.CO

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]

Shalosh B. Ekhad , Doron Zeilberger This is my paper

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keywords worldanalogenumerationgoalsgrouprichardstanleyalgebraic

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This short tribute to the guru of Enumerative and Algebraic Combinatorics started out when one the authors(DZ) attended the Stanely@70 conference, that took place at the same time as the preliminary stage of the 2014 World Cup. It states a surprising application of an analog of Richard Stanley's famous theorem about the enumeration of magic squares to the enumeration of possible outcomes in a World Cup Group.

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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]

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