通过牛顿方法计算$n$皇后常数的更紧界
Computing Tighter Bounds on the $n$-Queens Constant via Newton's Method
AI总结：
本文基于Simkin的凸优化公式与Knuth的更紧界，采用可扩展至大规模实例的牛顿方法，进一步计算出$n$皇后问题指数的更紧边界。
摘要：
近期Simkin的工作表明，著名$n$皇后问题中出现的指数界可通过求解凸优化问题来评估，使他找到了远比已知更紧的界。在本文中，我们使用Simkin的公式、Knuth开发的更紧界，以及可扩展至大规模问题实例的牛顿方法，找到了更紧的界。
英文摘要：
In recent work Simkin shows that bounds on an exponent occurring in the famous $n$-queens problem can be evaluated by solving convex optimization problems, allowing him to find bounds far tighter than previously known. In this note we use Simkin's formulation, a sharper bound developed by Knuth, and a Newton method that scales to large problem instances, to find even sharper bounds.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
