1月16日 范益政教授学术报告（数学与统计学院）

Let $G$ be a $t$-uniform hypergraph, and let $c(G)$ denote the cyclic index of the adjacency tensor of $G$. Let $m,s,t$ be positive integers such that $t \ge 2$,$s \ge 2$ and $m=st$. The generalized power $G^{m,s}$ of $G$ is obtained from $G$ by blowing up each vertex into an $s$-set and preserving the adjacencyrelation. It was conjectured that $c(G^{m,s})=s \cdot c(G)$. In this paper we show that the conjecture is false by giving a counter example, and give some sufficient conditions for the conjecture holding. Finally we give an equivalent characterization of the equality in the conjecture by using a matrix equation over $\mathbb{Z}_m$.

范益政，教授，博士，博士生导师，教育部新世纪优秀人才，安徽省学术和技术带头人，中国工业与应用数学学会图论组合及应用专业委员会副主任委员，中国运筹学会图论组合学分会常务理事，中国数学会图论与组合专业委员会委员，安徽省数学会常务理事，安徽大学数学科学学院院长。主要研究方向：代数组合与谱图理论。主持国家自然科学基金项目，发表论文100余篇。

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