On resolvable Golomb rulers, symmetric configurations and progressive dinner parties

We define a new type of Golomb ruler, which we term a resolvable Golomb ruler . These are Golomb rulers that satisfy an additional “resolvability” condition that allows them to generate resolvable symmetric configurations . The resulting configurations give rise to progressive dinner parties . In th...

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Bibliographic Details
Published in:Journal of algebraic combinatorics 2022-02, Vol.55 (1), p.141-156
Main Authors: Buratti, Marco, Stinson, Douglas R.
Format: Article
Language:English
Subjects:
Combinatorics
Computer Science
Configurations
Convex and Discrete Geometry
Group Theory and Generalizations
Lattices
Mathematics
Mathematics and Statistics
Order
Ordered Algebraic Structures
Wines
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Summary:We define a new type of Golomb ruler, which we term a resolvable Golomb ruler . These are Golomb rulers that satisfy an additional “resolvability” condition that allows them to generate resolvable symmetric configurations . The resulting configurations give rise to progressive dinner parties . In this paper, we investigate existence results for resolvable Golomb rulers and their application to the construction of resolvable symmetric configurations and progressive dinner parties. In particular, we determine the existence or nonexistence of all possible resolvable symmetric configurations and progressive dinner parties having block size at most 13, with nine possible exceptions. For arbitrary block size k , we prove that these designs exist if the number of points is divisible by k and at least k 3 .
ISSN:0925-9899
1572-9192
DOI:10.1007/s10801-020-01001-x