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

计算技术正在发展， 组合配置，特别是：t-设计和拉姆齐 号码 在这两种情况下使用的搜索算法是 类似的是计算技术和理论工具。 在 最近的工作，PI发现了一个显着的特殊设计，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， 继续计算。 在他们最近关于Ramsey图的工作中， 发现了Ramsey数的几个新的下界。 法律与正义党 现在正在探索几种新的方法来进一步改进 在上下界中。 希望他们能计算出 一个或多个小Ramsey数的值。 拟议的工作将继续进行主要研究员已开始的宝贵工作 在他们以前的RUI赠款期间，只有12个月 个月上一次赠款的结果得到了高度评价， 预期沿着同一条线的进一步结果是沿着的。 拟议工作 为相关学生提供了非常合适的体验。

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.