# $0\text{-}1$ sequences having the same numbers of $\left(1\text{-}1\right)$-couples of given distances

Antonín Lešanovský; Jan Rataj; Stanislav Hojek

Mathematica Bohemica (1992)

- Volume: 117, Issue: 3, page 271-282
- ISSN: 0862-7959

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topLešanovský, Antonín, Rataj, Jan, and Hojek, Stanislav. "$0\text{-}1$ sequences having the same numbers of $(1\text{-}1)$-couples of given distances." Mathematica Bohemica 117.3 (1992): 271-282. <http://eudml.org/doc/29442>.

@article{Lešanovský1992,

abstract = {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 $\delta ^\{(a)\}=\delta ^\{(b)\}$.},

author = {Lešanovský, Antonín, Rataj, Jan, Hojek, Stanislav},

journal = {Mathematica Bohemica},

keywords = {uniform distribution; set covariance; $0\text\{-\}1$ sequence; distance sequence; uniform distribution; set covariance; 0–1 sequence; distance sequence},

language = {eng},

number = {3},

pages = {271-282},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {$0\text\{-\}1$ sequences having the same numbers of $(1\text\{-\}1)$-couples of given distances},

url = {http://eudml.org/doc/29442},

volume = {117},

year = {1992},

}

TY - JOUR

AU - Lešanovský, Antonín

AU - Rataj, Jan

AU - Hojek, Stanislav

TI - $0\text{-}1$ sequences having the same numbers of $(1\text{-}1)$-couples of given distances

JO - Mathematica Bohemica

PY - 1992

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 117

IS - 3

SP - 271

EP - 282

AB - 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 $\delta ^{(a)}=\delta ^{(b)}$.

LA - eng

KW - uniform distribution; set covariance; $0\text{-}1$ sequence; distance sequence; uniform distribution; set covariance; 0–1 sequence; distance sequence

UR - http://eudml.org/doc/29442

ER -

## References

top- 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. (1990)
- W. Nagel, The uniqueness of a planar convex polygon when its set covariance is given, Forschungsergebnisse N/89/17, Friedrich-Schiller-Universität, Jena, 1989. (1989)
- R. Pyke, Problems corner, The IMS Bulletin 18 no. 3 (1989), 347. (1989)
- R. Pyke, Problems corner, The IMS Bulletin 18 no. 4 (1989), 387. (1989)
- J. Serra, Image Analysis and Mathematical Morphology, Academic Press, London, 1982. (1982) Zbl0565.92001MR0753649

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