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- W1588607283 abstract "The $n$-card problem is to determine the minimal intervals $[u,v]$ such that for every $n times n$ stochastic matrix $A$ there is an $n times n$ permutation matrix $P$ (depending on $A$) such that tr$(PA) in [u,v]$. This problem is closely related to classical mathematical problems from industry and management, including the linear assignment problem and the travelling salesman problem. The minimal intervals for the $n$-card problem are known only for $n le 4$.We introduce a new method of analysis for the $n$-card problem that makes repeated use of the Extreme Principle. We use this method to answer a question posed by Sands (2011), by showing that $[1,2]$ is a solution to the $n$-card problem for all $n ge 2$. We also show that each closed interval of length $frac{n}{n-1}$ contained in $[0,2)$ is a solution to the $n$-card problem for all $n ge 2$." @default.
- W1588607283 created "2016-06-24" @default.
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- W1588607283 date "2012-06-28" @default.
- W1588607283 modified "2023-09-26" @default.
- W1588607283 title "The $n$-Card Problem, Stochastic Matrices, and the Extreme Principle" @default.
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- W1588607283 doi "https://doi.org/10.37236/2444" @default.
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