Geodesic
$0\text{-}1$ sequences having the same numbers of $(1\text{-}1)$-couples of given distances
Mathematica Bohemica, Tome 117 (1992) no. 3, pp. 271-282

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MR Zbl
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 $\delta^{(a)}=\delta^{(b)}$.
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 $\delta^{(a)}=\delta^{(b)}$.
DOI : 10.21136/MB.1992.126288
Classification : 11B05, 11B83, 11K31
Keywords: uniform distribution; set covariance; $0\text{-}1$ sequence; distance sequence 
Lešanovský, Antonín; Rataj, Jan; Hojek, Stanislav. $0\text{-}1$ sequences having the same numbers of $(1\text{-}1)$-couples of given distances. Mathematica Bohemica, Tome 117 (1992) no. 3, pp. 271-282. doi: 10.21136/MB.1992.126288
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[1] A. Lešanovský, J. Rataj: Determination of compact sets in Euclidean spaces by the volume of their dilation. Proc. DIANA III, Bechyně, Czechoslovakia, June 4-8, 1990, Mathematical Institute of the ČSAV, Praha, 1990, pp. 165-177.

[2] W. Nagel: The uniqueness of a planar convex polygon when its set covariance is given. Forschungsergebnisse N/89/17, Friedrich-Schiller-Universität, Jena, 1989.

[3] R. Pyke: Problems corner. The IMS Bulletin 18 no. 3 (1989), 347.

[4] R. Pyke: Problems corner. The IMS Bulletin 18 no. 4 (1989), 387.

[5] J. Serra: Image Analysis and Mathematical Morphology. Academic Press, London, 1982. | MR | Zbl

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