论文标题
关于可分离的戈隆统治者，对称配置和进步晚宴
On Resolvable Golomb Rulers, Symmetric Configurations and Progressive Dinner Parties
论文作者
论文摘要
我们定义了一种新型的Golomb统治者，我们将其称为可分离的Golomb统治者。这些是满足额外的“可分辨率”条件的Golomb统治者，使他们能够生成可分辨出的对称配置。由此产生的配置引起了进步的晚宴。在本文中，我们调查了可分离的戈隆统治者的存在结果，并将其应用于建造可分配的对称配置和进步晚宴的构造。特别是，我们确定所有可能的可分离对称配置的存在或不存在，最多具有13个块大小的进步晚餐派对，有9个可能的例外。对于任意块大小k，我们证明，如果k和至少k^3可以分组的点数，则存在这些设计。
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.
