On resolvable Golomb rulers, symmetric configurations and progressive dinner parties

We define a new type of Golomb ruler, which we term resolvable ruler. These are rulers that satisfy an additional “resolvability” condition allows them to generate symmetric configurations. The resulting configurations give rise progressive dinner parties. In this paper, investigate existence results for and their application the construction particular, determine or nonexistence all possible parties having block size at most 13, with nine exceptions. For arbitrary k, prove these designs exist if number points is divisible by k least $$k^3$$ .