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math.CO2025
The discrete Laplace asymptotic method and its application to the 3XOR satisfiability problem
Jared A. Hughes, J. William Helton, Peter Schlosser
A standard way to calculate the asymptotic behavior of integrals of the form \int_Wg(x)e^{-nh(x)}dx is the (continuous) Laplace asymptotic method. However, also discrete sums like…
math.CO2025
The Satisfiability Threshold for K-XOR Games
Jared A. Hughes, J. William Helton
A -XORGAME system corresponds to a -XORSAT system with the additional restriction that the variables divide uniformly into blocks. This forms a system of equations wi…
math.CO2024
Uniform Convergence of an Asymptotic Approximation to Associated Stirling Numbers
E. Rodney Canfield, J. William Helton, Jared A. Hughes
Let be the -associated Stirling numbers of the second kind, the number of ways to partition a set of size into subsets of size at least . For , these…