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

Antonín Lešanovský; Jan Rataj; Stanislav Hojek

Mathematica Bohemica (1992)

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

Abstract

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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 ) .

How to cite

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Lešanovský, 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

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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. (1990) 
  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. (1989) 
  3. R. Pyke, Problems corner, The IMS Bulletin 18 no. 3 (1989), 347. (1989) 
  4. R. Pyke, Problems corner, The IMS Bulletin 18 no. 4 (1989), 387. (1989) 
  5. J. Serra, Image Analysis and Mathematical Morphology, Academic Press, London, 1982. (1982) Zbl0565.92001MR0753649

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