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math.CO2012
McMahon's Formula via Free Fermions
John Mangual
We give an elementary derivation of the vertex-operator derivation McMahon formula, counting all plane partitions of all size into a single generating function. We fill in some det…
math.GR2012
On the 5/8 bound for non-Abelian Groups
John Mangual
If we pick two elements of a non-abelian group at random, the odds this pair commutes is at most 5/8, so there is a "gap" between abelian and non-abelian groups \cite{G}. We prove…