报告题目：Periods of strongly connected multivariate digraphs
主讲人：吴耀琨
报告时间：10月19日 11:00-11:30
报告地点：西安电子科技大学南校区会议中心B101报告厅
For any positive integer $t$, a $t$-variable digraph on a set $K$ is a map $f$ from $K^t$ to $K$. As a qualitative counterpart of going from Markov chains to higher-order Markov chains, Wu, Xu and Zhu suggested in 2017 a study of $t$-variable digraphs, viewing usual digraphs as $1$-variable digraphs. Each strongly connected digraph has a period; this fact indeed extends to all strongly connected $t$-variable digraphs. Let $\mathcal{P\mkern-2mu S}(t)$ denote the set of all periods of strongly connected $t$-variable digraphs, let $g (t)$ be its Frobenius number, namely the largest nonnegative integer that is not a member of $\mathcal{P\mkern-2mu S}(t)$, and let $n(t)$ be its Sylvester number, namely the number of positive integers outside of $\mathcal{P\mkern-2mu S}(t)$. We provide new estimates for $g (t)$ and $n(t)$. We also find that $\mathcal{P\mkern-2mu S}(t)\cap \{1,2,\ldots, 4t-1\}$ is $\{1,8\}$ and $\{1\}$ when $t\in \{3,4\}$ and $t\geq 5$, respectively. Joint work with Chengyang Qian and Yinfeng Zhu.
吴耀琨，2002年上海交大博士毕业，遂留校任教至今。日常工作围绕单位安排的课程以及班上学生来展开，尽其所能来学习一些适合与有好奇心的高中生和低年级大学生一起思考的组合学题材。
