RUI: Computing Combinatorial Configurations: t-Designs & Ramsey Numbers

人们正在开发计算技术来发现难以捉摸的组合构型，特别是：t型设计和拉姆齐数。在这两种情况下使用的搜索算法是相似的，计算技术和理论工具也是相似的。在最近的工作中，pi发现了一个值得注意的特殊设计以及一个新的设计家族。他们现在正在改进所使用的技术，开发新的实现，并构建新的算法来继续他们的计算。在他们最近对拉姆齐图的研究中，他们发现了拉姆齐数的几个新的下界。pi现在正在探索几种新方法，以进一步改进下界和上界。人们希望他们能计算出一个或多个小拉姆齐数的精确值。拟议的工作将继续pi在先前的RUI资助期间开始的宝贵工作，该资助仅持续12个月。前一次赠款的结果得到了高度评价，预计今后也会取得同样的结果。建议的工作为相关的学生提供了非常合适的经验。

Computational techniques are being developed for discovering elusive combinatorial configurations, specifically: t-designs and Ramsey numbers. The search algorithms being employed in the two cases are similar as are the computational techniques and theoretical tools. In recent work the PIs have found a notable special design as well as a new family of designs. They are now refining the techniques used, developing new implementations, and constructing new algorithms to continue their computations. In their recent work on Ramsey graphs several new lower bounds were discovered for Ramsey numbers. The PIs are now exploring several new approaches for making further improvements in lower and upper bounds. It is hoped that they will compute the exact value of one or more of the small Ramsey numbers. The proposed work will continue the valuable work that the PIs started during their previous RUI grant which was for a period of only 12 months. The results of the previous grant have been highly rated and further results along the same line are anticipated. The proposed work provides very appropriate experience for the students involved.