# The number of $n$-queens configurations

@inproceedings{Simkin2021TheNO, title={The number of \$n\$-queens configurations}, author={Michael Simkin}, year={2021} }

The n-queens problem is to determine Q(n), the number of ways to place n mutually non-threatening queens on an n×n board. We show that there exists a constant α = 1.942±3×10−3 such that Q(n) = ((1 ± o(1))ne−α)n. The constant α is characterized as the solution to a convex optimization problem in P([−1/2, 1/2]), the space of Borel probability measures on the square. The chief innovation is the introduction of limit objects for n-queens configurations, which we call queenons. These are a convex… Expand

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