4 papers
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…
math.NT2008
Duke's Theorem and Continued Fractions
John Mangual
For uniformly chosen random , it is known the probability the digit of the continued-fraction expansion, converges to the Gauss-Kuzmin distribution…
math.CA2007
Uniform Convergence Behavior of the Bernoulli Polynomials
John Mangual
The roots of Bernoulli polynomials, , when plotted in the complex plane, accumulate around a peculiar H-shaped curve. Karl Dilcher proved in 1987 that, on compact subsets o…