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 \(k^3\).

我们定义了一种新型的Golomb标尺，我们称其为可解析的Golomb标尺。这些是Golomb直尺，可以满足额外的“可分辨性”条件，使它们能够生成可分辨的对称构型。最终的配置导致进行渐进式晚宴。在本文中，我们调查了可解决的哥伦布尺子的存在结果及其在可解决的对称配置和渐进式宴会中的应用。特别是，我们确定是否存在所有可能的可解决的对称配置以及具有最多13个块大小的渐进式晚餐聚会，其中有九种可能的例外。对于任意块大小k，我们证明了如果点的数量可被k整除且至少为\（k ^ 3 \），则这些设计存在。