AI 中文总结
本文研究施泰纳三元系（STS）的燃烧与延迟燃烧过程，得到其燃烧数的对数界，证明存在任意ρ≥3的STS具有燃烧数ρ，发现延迟燃烧等价于STS维数，还研究了仿射、射影三元系的相关数。
AI 中文摘要
图燃烧是一种基于回合的过程，可视为模拟网络中影响力传播的离散单人游戏。将该过程扩展到超图有多种方式，已研究的两种此类过程包括超图的燃烧过程和延迟燃烧过程。组合设计可被视为具有有用且有趣特性的超图。本文研究了施泰纳三元系（STS）中的燃烧和延迟燃烧过程，得到了任意STS的燃烧数的对数界，并证明了对于任意整数ρ≥3，存在燃烧数为ρ的STS。我们发现延迟燃烧的概念等价于STS的维数概念，并探讨了这种等价性的影响；还证明了施泰纳三元系的燃烧数与延迟燃烧数的差值可以任意大。最后，我们详细研究了仿射三元系和射影三元系的燃烧数与延迟燃烧数。
英文摘要
Graph burning is a round-based process which can be viewed as a discrete one-player game that models the spread of influence throughout a network. Extending this process to hypergraphs can be done in numerous ways; two such processes that have been studied include the burning process and the lazy burning process for hypergraphs. Combinatorial designs can be thought of as hypergraphs with useful and interesting characteristics. In this paper we explore the burning and lazy burning processes in Steiner triple systems (STSs). We obtain logarithmic bounds on the burning number of an arbitrary STS and prove the existence of an STS with burning number $ρ$ for any integer $ρ\geq 3$. We observe that the concept of lazy burning is equivalent to the notion of the dimension of an STS, and we consider ramifications of this equivalence. We also show that the difference between the burning and lazy burning number of a Steiner triple system can be arbitrarily large. Finally, we consider burning and lazy burning numbers of affine and projective triple systems in detail.
Comments22 pages
