Article
Full entry |
PDF
(1.3 MB)
Feedback
PDF
(1.3 MB)
Feedback
Keywords:
uniform distribution; set covariance; $0\text{-}1$ sequence; distance sequence
uniform distribution; set covariance; $0\text{-}1$ sequence; distance sequence
Summary:
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 $\delta^{(a)}=\delta^{(b)}$.
References:
[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 0753649 | Zbl 0565.92001
Search
Partner of
