论文标题
最大熵和整数分区
Maximum entropy and integer partitions
论文作者
论文摘要
我们为$ j $ th powers的整数分区的数量得出了渐近公式，该零件的零件为$ j $，属于有限的，非空的套件$ j \ subset \ subset \ mathbb n $。我们使用的方法基于Jaynes的“最大熵原理”。该原理导致了一个直观的变分公式，用于对对数的渐近分区数量的渐近图作为对实现函数的凸优化问题的解决方案。
We derive asymptotic formulas for the number of integer partitions with given sums of $j$th powers of the parts for $j$ belonging to a finite, non-empty set $J \subset \mathbb N$. 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.
