then they obey a lot of relationships, abc=def
a+1=b,a+3=cd+1=e,d−1=f
abc+bca+acb−(def+efd+dfe)=2(a−d)=2(b−e)=2(c−f−4)
as well as
(4abc+bca)+2a=abc+bca+acb(4def+efd)+2d=def+efd+dfe(4abc+bca)+2cde−2=abc+def+(cde−3ecd)
and so on. Combining the last three relations by getting rid of the red non-moonshine terms yields the most complicated of the 9 dependencies found by Conway, Norton, and Atkin such that the monster functions span a linear space of 172−9=163 dimensions.
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