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- W4300561567 abstract "In this paper, we derive simple closed-form expressions for the $n$-queens problem and three related problems in terms of permanents of $(0,1)$ matrices. These formulas are the first of their kind. Moreover, they provide the first method for solving these problems with polynomial space that has a nontrivial time complexity bound. We then show how a closed-form for the number of Latin squares of order $n$ follows from our method. Finally, we prove lower bounds. In particular, we show that the permanent of Schur's complex valued matrix is a lower bound for the toroidal semi-queens problem, or equivalently, the number of transversals in a cyclic Latin square." @default.
- W4300561567 created "2022-10-03" @default.
- W4300561567 creator A5087298778 @default.
- W4300561567 date "2016-09-29" @default.
- W4300561567 modified "2023-09-27" @default.
- W4300561567 title "Closed-Form Expressions for the n-Queens Problem and Related Problems" @default.
- W4300561567 doi "https://doi.org/10.48550/arxiv.1609.09585" @default.
- W4300561567 hasPublicationYear "2016" @default.
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