报告人：李峰伟 副教授（ 绍兴文理学院）
时 间：2018年6月30日（周六）下午15:30 - 16：30
题 目：On AZI index of F-benzenoid Systems
摘 要：In theoretical chemistry and biology, molecular descriptors are used for modeling structural information of molecules, with the purpose of capturing interesting physical and chemical properties of these molecules in single numerical values. These molecular descriptors are also referred to as topological indices. In this presentation, we study the augmented Zagreb index (AZI index for short), which has been proven to be a valuable predictive index in the study of the heat of formation in octanes and heptanes. We give an expression for the AZI index of f-benzenoid systems in terms of their inlet features, and deduce the minimal and maximal value of the AZI index over the set of cata-catacondensed f-benzenoid systems. We also discuss the minimal values of the AZI indices of f-benzenoid systems with a given number of hexagons. Finally, we present several sharp upper bounds on the AZI index of graphs with fixed parameters such as the independence number, the edge-connectivity and the chromatic number respectively, and characterize the corresponding extremal graphs.
报告人：周大跑 博士 （ 绍兴文理学院）
时 间：2018年6月30日（周六）下午16:30 - 17：30
题 目：The Raney Numbers and (s,s+1)-core Partitions
摘 要：The Raney numbers Rp,r(k) are a two-parameter generalization of the Catalan numbers.
In this paper, we give a combinatorial proof for a recurrence relation of the Raney numbers in terms of coral diagrams. Using this recurrence relation, we confirm a conjecture posed by Amdeberhan concerning the enumeration of (s, s+1)-core partitions with parts that are multiples of p. As a corollary, we give a new combinatorial interpretation for the Raney numbers Rp+1,r+1(k) with 0r<p in terms of (kp+r,kp+r+1)-core partitions with parts that are multiples of p.