2020/12/28 by Gweneth McKinley, McKinley, Gweneth, Marcus Michelen +3
Mathematics · #Mathematical Dynamics and Fractals #Functional Equations Stability Results #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2012.14498
We derive asymptotic formulas for the number of integer partitions with given sums of jth powers of the parts for j belonging to a finite, non-empty set J ⊂ \mathbb N. The method we use is based on the `principle of maximum entropy' of Jaynes. This principle leads to an intuitive variational formula for the asymptotics of the logarithm of the number of constrained partitions as the solution to a convex optimization problem over real-valued functions.