数学学科学术报告(李峰伟 绍兴文理学院 周大跑 绍兴文理学院))

发布者:段玉玲   发布时间:2018-06-29  浏览次数:148

报告一

报 告 人:李峰伟 副教授( 绍兴文理学院)

报告题目:On AZI index of F-benzenoid Systems

报告时间:本周六(2018.06.30)下午15:30 - 1630

报告地点:21-427

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.

  

报告二

报 告 人:周大跑 博士 ( 绍兴文理学院)

报告题目:The Raney Numbers and (s,s+1)-core Partitions

报告时间:本周六(2018.06.30)下午16:30 - 1730

报告地点:21-427

  

The Raney numbers $R_{p,r}(k)$ 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 $\lambda$ with parts that 

are multiples of p. As a corollary, we give a new combinatorial interpretation for the Raney 

numbers $R_{p+1,r+1}(k)$ with $0\leq r<p$ in terms of $(kp+r,kp+r+1)$-core partitions 

$\lambda$ with parts that are multiples of p.

  

  

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