This is the homepage of the SUSTech Discrete Mathematics Seminar at the Department of Mathematics at SUSTech.
The SUSTech Discrete Mathematics Seminar is organized by Ferdinand Ihringer, Caiheng Li, Qing Xiang, and Ziqing Xiang.
You can contact us under discretemath@sustech.edu.cn.
Speaker: Weigen Yan (Jimei University)
Room: College of Science M1001
Time: 2025/05/22, Thursday, 10:00 - 11:00
Tencent Meeting: 498 500 227
图的 dimer 问题是统计物理学家计算可解模型的热门研究对象, 与此相关的计数研究是组合学家十分关心的问题, 但解此问题很难，其中还有很多尚未解决的问题。报告首先将简单介绍此问题的一些经典结果，然后介绍我们最近得到的3维Sierpinski gasket的dimer问题的解公式。
Speaker: Sergey Goryainov (Hebei Normal University)
Room: College of Science M1001
Time: 2025/05/15, Thursday, 10:00 - 11:00
Tencent Meeting: 876 235 785
Divisible designs graphs (DDGs for short) were introduced in 2011 by Haemers, Kharaghani and Meulenberg as a bridge between graph theory and the theory of (group divisible) designs. Since then, around 20 constructions producing infinitely many DDGs haven been introduced. These constructions make use of many combinatorial and algebraic objects: finite geometries, Hadamard matrices, weighing matrices, designs, Cayley graphs, block matrices, strongly regular graphs and so on. Also, a number of characterisations of divisible design graphs is known. In this talk we will discuss three infinite families of DDGs recently discovered in connection with symplectic spaces. The talk is based on joint works with Anwita Bhowmik, Bart De Bruyn, Willem Haemers and Leonid Shalaginov.
Speaker: Jianfeng Hou (Fuzhou University)
Room: College of Science M1001
Time: 2025/05/08, Thursday, 10:00 - 11:00
Tencent Meeting: 243 241 628
For a nondegenerate r-graph F, large n, and t in the regime [0, cF n], where cF > 0 is a constant depending only on F, we present a general approach for determining the maximum number of edges in an n-vertex r-graph that does not contain t + 1 vertex-disjoint copies of F. In fact, our method results in a rainbow version of the above result and includes a characterization of the extremal constructions. Our approach applies to many well-studied hypergraphs (including graphs) such as the edge-critical graphs, the Fano plane, the generalized triangles, hypergraph expansions, the expanded triangles, and hypergraph books. Our results extend old results of Erd˝os, Simonovits, and Moon on complete graphs, and can be viewed as a step towards a general density version of the classical Corr´adi–Hajnal and Hajnal–Szemer´edi Theorems. Our method relies on a novel understanding of the general properties of nondegenerate Tur´an problems, which we refer to as smoothness and boundedness. These properties are satisfied by a broad class of nondegenerate hypergraphs and appear to be worthy of future exploration (Join work with Heng Li, Xizhi Liu, Long-Tu Yuan and Yixiao Zhang).
Speaker: Xianwei Xia (Suzhou University of Science and Technology)
Room: College of Science M1001
Time: 2025/04/17, Thursday, 10:00 - 11:00
Tencent Meeting: 329 689 224
In their study of the truncated sums of the classical theta functions, Andrews-Merca and Guo-Zeng posed a conjecture on truncated sums of a special case of the Jacobi triple product identity which was confirmed independently by Mao and Yee. In 2016, Chan, Ho and Mao examined the truncated series arising from two consequences of the quintuple product identity. In this talk, we establish an explicit series form with nonnegative coefficients on a new truncated sum of a special cases of the Jacobi triple product identity by taking different truncated series which is stronger than the conjecture due to Andrews-Merca and Guo-Zeng. As a corollary of our results, we obtain a new truncated sums of Jacibi’s identity which implies another conjecture given by Guo and Zeng. In addition, we determine the signs of coefficients of new truncated sums of two well-known identities derived from the quintuple product identity which can be considered as the companion results of a theorem proved by Chan, Ho and Mao.
Speaker: Congpei An (Guizhou University)
Room: College of Science M1001
Time: 2025/04/15, Tuesday, 14:00 - 15:00
Tencent Meeting: 237 114 541
We discuss the approximation of continuous functions on the unit sphere by spherical polynomials of degree n via hyperinterpolation. Hyperinterpolation of degree n is a discrete approximation of the L2-orthogonal projection of degree n with its Fourier coefficients evaluated by a positive-weight quadrature rule that exactly integrates all spherical polynomials of degree at most 2n. This talk aims to bypass this quadrature exactness assumption by replacing it with the Marcinkiewicz–Zygmund property. Consequently, hyperinterpolation can be constructed by a positive-weight quadrature rule–not necessarily with quadrature exactness. This scheme is called unfettered hyperinterpolation. We provide a reasonable error estimate for unfettered hyperinterpolation. The error estimate generally consists of two terms: a term representing the error estimate of the original hyperinterpolation of full quadrature exactness and another introduced as compensation for the loss of exactness degrees. A guide to controlling the newly introduced term in practice is provided. In particular, if the quadrature points form a quasi-Monte Carlo design, then there is a refined error estimate. Numerical experiments verify the error estimates and the practical guide.
Speaker: Andrey Kupavskii (Moscow Institute of Physics and Technology)
Room: College of Science M4009
Time: 2025/04/10, Thursday, 10:00 - 11:00
Tencent Meeting: 298 668 764
I will speak about the recent progress on the Erdos-Ko-Rado type results for different structures that we have managed to obtain using the method of spread approximations. I’ll mostly focus on partitions and, in particular, the resolution of the Meagher-Moura question on partially t-intersecting families of partitions.