Corpus ID: 236469406

# 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

#### References

SHOWING 1-10 OF 25 REFERENCES
New bounds on the number of n-queens configurations
In how many ways can $n$ queens be placed on an $n \times n$ chessboard so that no two queens attack each other? This is the famous $n$-queens problem. Let $Q(n)$ denote the number of suchExpand
A survey of known results and research areas for n-queens
• Mathematics, Computer Science
• Discret. Math.
• 2009
This paper surveys known results for the n-queens problem of placing n nonattacking queens on an nxn chessboard and considers extensions of the problem, e.g. other board topologies and dimensions, and investigates a number of open research areas. Expand
An upper bound on the number of high-dimensional permutations
• Mathematics, Computer Science
• Comb.
• 2014
The main tool is an adaptation of Brégman’s proof of the Minc conjecture on permanents, and the main result is the following upper bound on the number of d-dimensional permutations: n n d. Expand
Counting solutions for the N -queens and Latin-square problems by Monte Carlo simulations.
• Mathematics, Physics
• Physical review. E, Statistical, nonlinear, and soft matter physics
• 2009
Monte Carlo simulations are applied to count the numbers of solutions of two well-known combinatorial problems: the N -queens problem and Latin-square problem to accelerate sampling. Expand
An Entropy Proof of Bregman's Theorem
A short proof of this theorem was given by Schrijver (J. Expand
Limits of permutation sequences
• R. Sampaio
• Computer Science, Mathematics
• J. Comb. Theory, Ser. B
• 2008
A permutation sequence (@s"n)"n"@?"N is said to be convergent if, for every fixed permutation @t, the density of occurrences of @t in the elements of the sequence converges. We prove that such aExpand
An upper bound on the number of Steiner triple systems
• Mathematics, Computer Science
• Random Struct. Algorithms
• 2013
This work shows how to derive the bound on the number of n -vertex Steiner triple systems using the entropy method and considers the number F(n) of 1 -factorizations of the complete graph on n vertices. Expand
On the Method of Typical Bounded Differences
• L. Warnke
• Computer Science, Mathematics
• Combinatorics, Probability and Computing
• 2015
A variant of the bounded differences inequality which can be used to establish concentration of functions f(X) where (i) the typical changes are small, although (ii) the worst case changes might be very large, is proved. Expand
Additive triples of bijections, or the toroidal semiqueens problem
• Mathematics
• 2015
We prove an asymptotic for the number of additive triples of bijections $\{1,\dots,n\}\to\mathbb{Z}/n\mathbb{Z}$, that is, the number of pairs of bijections $\pi_1,\pi_2\colonExpand The existence of designs via iterative absorption: hypergraph$F$-designs for arbitrary$F$. • Mathematics • 2020 We solve the existence problem for$F$-designs for arbitrary$r$-uniform hypergraphs~$F$. This implies that given any$r$-uniform hypergraph~$F\$, the trivially necessary divisibility conditions areExpand