Mathematics Abstracts of Presentations

Weighted Generalized Crank Moments for $k$-colored Partitions

Toh Pee Choon (National Institute of Education, Singapore)

In this talk, we will briefly introduce the concept of $k$-colored partitions and the associated generalized crank moments. Thereafter, we will present some results obtained by the author and his collaborators.

A Glimpse of Graph Colorings

Meiqiao Zhang (National Institute of Education, Singapore)

Graph coloring is one of the most important and long-standing topics in graph theory. Not only does it tie many concepts in graph theory in surprising ways, but it also has a wide range of real-world applications. In this talk, I will briefly introduce a few different kinds of graph colorings, along with some simple but fascinating results of them.

NRAFHDLT: A R package for the high-dimensional location testing problems with the normal-reference approach

Wang Pengfei (National Institute of Education, Singapore)

In this talk, we give the most current of methods based on normal reference approach to test the equality of the mean vectors of high-dimensional samples with possibly different covariance matrices. We conveniently group the methods into two categories which are two-sample problem and general linear hypothesis testing problem based on the number of samples. We offer some perspectives on the connections and distinctions among the tests. An $R$ package named NRAFHDLT is given to show the implementation of these tests and which also provides an easy and user-friendly access to the above tests. Simulated Type I error rates and powers of the sum-up tests are also shown. We illustrate the implemented procedures by two real examples from biology for different categories.

An Elementary Exploration of Knot Theory

Deng Qingying (Xiang Tan University, China)

Knot theory is a unique branch of mathematics dedicated to the study of the properties of closed curves or ropes. This elementary report provides an overview of the fundamental concepts of knot theory, including the definition and properties of knots. We briefly touch on its history and some practical applications to inspire an interest in this fascinating field of mathematics.

Polynomials of graphs

Fengming Dong (National Institute of Education, Singapore)

There are various polynomials of graphs, which reflect the structures and properties of graphs. In this talk, we will introduce some polynomials of graphs.