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Given distinct permutations $\\pi, \\sigma\\in \\Omega$, we let $hd(\\pi, \\sigma) = |\\{ x\\in \\Omega: \\pi(x) \\ne \\sigma(x) \\}|$, called the Hamming distance between $\\pi$ and $\\sigma$. Now let $hd(A) =$ min$\\{ hd(\\pi, \\sigma): \\pi, \\sigma \\in A \\}$. For positive integers $n$ and $d$ with $d\\le n$, we let $M(n,d)$ be the maximum number of permutations in any array $A$ satisfying $hd(A) \\geq d$. 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Sudborough, Linda Morales, Luis Gerardo Mojica, Sergey Bereg, Zevi Miller","submitted_at":"2018-04-11T01:02:32Z","abstract_excerpt":"A permutation array $A$ is a set of permutations on a finite set $\\Omega$, say of size $n$. Given distinct permutations $\\pi, \\sigma\\in \\Omega$, we let $hd(\\pi, \\sigma) = |\\{ x\\in \\Omega: \\pi(x) \\ne \\sigma(x) \\}|$, called the Hamming distance between $\\pi$ and $\\sigma$. Now let $hd(A) =$ min$\\{ hd(\\pi, \\sigma): \\pi, \\sigma \\in A \\}$. For positive integers $n$ and $d$ with $d\\le n$, we let $M(n,d)$ be the maximum number of permutations in any array $A$ satisfying $hd(A) \\geq d$. 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