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Enumeration of Golomb rulers
, 2011
"... Generally a ruler is marked in equal increments, e.g., a 12 inch ruler has 12 markings, each 1 inch apart. In this paper we discuss a special type of ruler discovered by Soloman W. Golomb. We define a Golomb ruler to be a ruler of length d with n markings where the distance between any two markings ..."
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Generally a ruler is marked in equal increments, e.g., a 12 inch ruler has 12 markings, each 1 inch apart. In this paper we discuss a special type of ruler discovered by Soloman W. Golomb. We define a Golomb ruler to be a ruler of length d with n markings where the distance between any two markings
GOLOMB RULERS AND GRACEFUL GRAPHS
"... Abstract. A Golomb ruler is a marked straightedge such that the distances between different pairs of marks on the straightedge are distinct. A graceful labeling of a simple graph G is an injection f from the vertices of G to the set {0, 1, 2,..., n}, where n is the number of edges of G, such that th ..."
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Abstract. A Golomb ruler is a marked straightedge such that the distances between different pairs of marks on the straightedge are distinct. A graceful labeling of a simple graph G is an injection f from the vertices of G to the set {0, 1, 2,..., n}, where n is the number of edges of G
Maximizing Irregularity and the Golomb Ruler Problem
, 1997
"... The problem of attempting to construct radar signals whose ambiguity functions are sharply peaked in both time and frequency gives rise to a quantitative concept of the irregularity of a distribution of points. The problem of maximizing the irregularity of N points distributed on a bounded closed in ..."
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the (continuous) irregularity function become questions about this integral construction, many of which can be answered easily and elegantly. One important question about the integral construction has been previously studied under the name of the Golomb Ruler Problem. It turns out that maximizing irregularity
Golomb Rulers
"... The Math Factor podcast posed the problem of finding the smallest number of inch marks on a 12 inch ruler so that one could still measure any integer length from 1 to 12. One needs only four additional marks besides 0 and 12; for example 1, 4, 7, 10 works. This entertaining problem lead to others du ..."
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Cited by 2 (0 self)
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during the next few minutes (you can listen at mathfactor.uark.edu/2005/10) and inspired us to look for generalizations. After several false starts and numerous literature searches we uncovered the fascinating theory of Golomb and minimal spanning rulers, a generalization to the natural numbers
Golomb Ruler
, 2003
"... Les textes publiés dans la série des rapports de recherche HEC n’engagent que la responsabilité de leurs auteurs. La publication de ces rapports de recherche bénéficie d’une subvention du Fonds québécois de la recherche sur la nature et les technologies. On the Design of Optimum Order 2 ..."
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Les textes publiés dans la série des rapports de recherche HEC n’engagent que la responsabilité de leurs auteurs. La publication de ces rapports de recherche bénéficie d’une subvention du Fonds québécois de la recherche sur la nature et les technologies. On the Design of Optimum Order 2
Wireless Communications
, 2005
"... Copyright c ○ 2005 by Cambridge University Press. This material is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University ..."
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Cited by 1129 (32 self)
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Copyright c ○ 2005 by Cambridge University Press. This material is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University
Enumeration of golomb rulers and acyclic orientations of mixed graphs
"... Dedicated to our friend and mentor Joseph Gubeladze on the occasion of his 50 th birthday A Golomb ruler is a sequence of distinct integers (the markings of the ruler) whose pairwise differences are distinct. Golomb rulers, also known as Sidon sets and B2 sets, can be traced back to additive number ..."
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Cited by 3 (1 self)
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Dedicated to our friend and mentor Joseph Gubeladze on the occasion of his 50 th birthday A Golomb ruler is a sequence of distinct integers (the markings of the ruler) whose pairwise differences are distinct. Golomb rulers, also known as Sidon sets and B2 sets, can be traced back to additive number
Analysis Of The Golomb Ruler And The Sidon Set Problems And Determination Of Large NearOptimal Golomb Rulers
, 2002
"... Golomb rulers have extensive uses in communications, from optimal spectrum allocation, to antenna design. This work presents efficient algorithms for the creation of near optimal rulers with a high number of marks. Furthermore, this work computationally extends the search for subquadratic rulers fr ..."
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Cited by 18 (0 self)
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Golomb rulers have extensive uses in communications, from optimal spectrum allocation, to antenna design. This work presents efficient algorithms for the creation of near optimal rulers with a high number of marks. Furthermore, this work computationally extends the search for subquadratic rulers
Results 1  10
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