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math.CO2020
The first families of highly symmetric Kirkman Triple Systems whose orders fill a congruence class
Simona Bonvicini, Marco Buratti, Martino Garonzi +2
Kirkman triple systems (KTSs) are among the most popular combinatorial designs and their existence has been settled a long time ago. Yet, in comparison with Steiner triple systems,…
math.CO2020
New Results on Modular Golomb Rulers, Optical Orthogonal Codes and Related Structures
Marco Buratti, Douglas R. Stinson
We prove new existence and nonexistence results for modular Golomb rulers in this paper. We completely determine which modular Golomb rulers of order exist, for all ,…
math.CO2020
On Resolvable Golomb Rulers, Symmetric Configurations and Progressive Dinner Parties
Marco Buratti, Douglas R. Stinson
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 gene…