2020/04/08 by Marco Buratti, Douglas R. Stinson, Buratti, Marco +1
Engineering · Mathematics · #05B05 #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2004.04088
openalex publication_date 2020/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define a new type of Golomb ruler, which we term a resolvable Golomb\nruler. These are Golomb rulers that satisfy an additional "resolvability"\ncondition that allows them to generate resolvable symmetric configurations. The\nresulting configurations give rise to progressive dinner parties. In this\npaper, we investigate existence results for resolvable Golomb rulers and their\napplication to the construction of resolvable symmetric configurations and\nprogressive dinner parties. In particular, we determine the existence or\nnonexistence of all possible resolvable symmetric configurations and\nprogressive dinner parties having block size at most 13, with nine possible\nexceptions. For arbitrary block size k, we prove that these designs exist if\nthe number of points is divisible by k and at least k3.\n