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**There are no new homometric Golomb ruler pairs with 12 marks or less.**
*(English)*
Zbl 0837.51009

A ruler with \(n + 1\) marks, such that each set of adjacent marks measures different distances is called “Golomb ruler” with \(n\) segments. Two such rulers are called homometric, if all distances both rulers are able to measure are the same. As a reflection of one ruler gives a homometric one in a trivial way, the article is restricted to the “nontrivial” cases. For the case \(n = 5\) such pairs of homometric rules are known. The authors in this article show, that for \(6 \leq n \leq 11\) nontrivial pairs of homometric rulers to not exist. This is done by a computer search following an algorithm, which is described in the paper.

Reviewer: Otto Röschel (Graz)

### Keywords:

rulers with finite marks
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\textit{E. Postpischil} and \textit{P. Gilbert}, Exp. Math. 3, No. 2, 147--152 (1994; Zbl 0837.51009)

### References:

[1] | DOI: 10.1038/scientificamerican1285-16 · doi:10.1038/scientificamerican1285-16 |

[2] | DOI: 10.1109/18.50388 · doi:10.1109/18.50388 |

[3] | Yovanof G. S., Ph.D. Dissertation, in: ”Homometric structures” (1988) |

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