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关于举行冯弢教授(北京交通大学)学术报告的通知

发布时间:2022-05-10文章来源:华南理工大学数学学院浏览次数:235

报告主题:Difference families: algebraic aspects and extremal aspects

 人:冯弢教授

报告时间:2022年5月12日(星期四)16:00-17:00

报告地点:腾讯会议,会议号896 460 214

 人:陈博聪教授


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数学学院

                                              20225月10日


报告摘要:Even though Peltesohn proved that a cyclic (v,3,1)-design exists if and only if v ≡ 1,3 (mod 6) as early as 1939, the problem of determining the spectrum of cyclic (v,k,1)-designs with k>3 is far from being settled, even for k=4. By exploring the underlying structure of difference families, we show that a cyclic (v,4,1)-design exists if and only if v ≡ 1,4 (mod 12) and v≠16, 25, 28.By giving previously unknown a pair of orthogonal orthomorphisms of cyclic groups of order 18t+9 for any positive integer t, we complete the existence spectrum of a pair of orthogonal orthomorphisms of cyclic groups. As a corollary, we complete the existence spectrum of a (G,4,1)-difference matrix over any finite abelian group G. Let D2H be the generalized dihedral group of an abelian group H. It is proved that a (D2H, 4, 1)-difference matrix exists if and only if H is of even order and H is not isomorphic to Z4. It is proved that if G is a finite abelian group and the Sylow 2-subgroup of G is trivial or noncyclic, then a (G,5,1)-DM exists except for some possible exceptions.Novak conjectured in 1974 that for any cyclic Steiner triple systems of order v with v ≡ 1 (mod 6), it is always possible to choose one block from each block orbit so that the chosen blocks are pairwise disjoint. We generalize this conjecture to cyclic (v, k,λ)-designs with 1≤λ≤k-1. We confirm that the generalization of the conjecture holds when v is a prime andλ=1 by using Combinatorial Nullstellensatz, and also whenλ≤ (k-1)/2 and v is sufficiently large compared to k by using proper edge-coloring of hypergraphs


报告人介绍冯弢,北京交通大学数学与统计学院教授,博士生导师主要研究方向为组合学与编码理论。在J. Combin. Theory Ser. A、IEEE Transactions on Information Theory、Science China Mathematics、Designs Codes and Cryptography、Finite Fields and Their ApplicationsDiscrete Mathematics等期刊发表论文篇;先后主持国家自然科学基金项目3项。