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11-XX Number theory
11Kxx Probabilistic theory: distribution modulo $1$ ; metric theory of algorithms
11K31 Special sequences

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$0 - 1$ sequences having the same numbers of $(1 - 1)$ -couples of given distances

Antonín Lešanovský, Jan Rataj, Stanislav Hojek (1992)

Mathematica Bohemica

Let $a$ be a $0 - 1$ sequence with a finite number of terms equal to 1. The distance sequence $δ^{(a)}$ 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 $δ^{(a)} = δ^{(b)}$ .

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