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uniform distribution; set covariance; $0\text{-}1$ sequence; distance sequence
Let $a$ be a $0-1$ sequence with a finite number of terms equal to 1. The distance sequence $\delta^{(a)}$ of $a$ is defined as a sequence of the numbers of $(1-1)$-couples of given distances. The paper investigates such pairs of $0-1$ sequences $a,b$ that a is different from $b$ and $\delta^{(a)}=\delta^{(b)}$.
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