报告人：关夏夏（太原理工大学）
报告时间：2025年9月23日（周二）16：00
报告地点：章辉楼442
联系人：马天龙
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报告摘要：The Tutte polynomial is an important invariant of graphs and matroids. Chen and Guo obtained a relation between coefficients of
and its minimal edge cuts of the graph G via the Abelian sandpile model, where
is the Tutte polynomial of the graph G. Recently, Ma, Guan and Jin generalized this result from graphs to matroids and obtained the dual result at the same time. In 2013, as a generalization of
and of graphs G to hypergraphs, Kálmán introduced interior and exterior polynomials for connected hypergraphs. Chen and Guo posed a problem that can one generalize these results to interior and exterior polynomials of hypergraphs? In this talk, we solve it in the affirmative by obtaining results for more general polymatroids, which also generalize the results due to Ma, Guan and Jin. Moreover, the sequence consisting of these coefficients is proven to be unimodal.
报告人简介：关夏夏，太原理工大学数学学院，硕士生导师。2023年博士毕业于厦门大学，曾赴日本东京工业大学进行访问交流一年。主要从事Tutte多项式和结构图论等研究工作。主持国家自然科学基金青年项目和山西省自然科学基金各一项，在Int. Math. Res. Not., J. Combin. Theory Ser. A，Adv. in Appl. Math. 等期刊上发表论文10余篇。
