A necessary condition for the existence of equitable partitions
主 讲 人 ：Denis Krotov 首席研究员
活动时间：09月25日14时00分
地 点 ：理科群1号楼D203室
讲座内容：
An equitable k-partition of a graph G is a partition (V1, ..., Vk) of the vertex set of G into k nonempty subsets such that for any i and j in {1,...,k} every vertex from Vi has exactly S(i,j) neighbors in Vj, where the coefficient S(i,j) depends only on i and j but not on the particular choice of the vertex in Vi. The k-by-k table of all coefficients S(i,j) is called the quotient matrix. In terms of eigenfunctions of the quotient matrix S, we describe a new necessary condition on the existence of equitable partitions in a concrete graph G. More details can be found at https://www.researchgate.net/publication/38204290_Completely_Regular_Codes_and_Equitable_Partitions (this is a chapter, j.w. with Vladimir Potapov, in the forthcoming book "Completely Regular Codes in Distance-Regular Graphs").
主讲人介绍：
He was born in Novosibirsk, Russia. He received the Bachelor's degree in mathematics in 1995 and the Master's degree in 1997, both from Novosibirsk State University, the Ph.D. and Dr.Sc. degrees in Discrete Mathematics and Theoretical Cybernetics from Sobolev Institute of Mathematics, Novosibirsk, in 2000 and 2011, respectively. Since 1997, he has been with Theoretical Cybernetics Department, Sobolev Institute of Mathematics, where he is currently a Chief Researcher. Since 2012, he has been a Professor of the Russian Academy of Science. In 2003, he was a Visiting Researcher with Pohang University of Science and Technology, Korea. For several months in 2018-2023, he was a visiting professor in Anhui University, Hefei, China. His research interest includes subjects related to discrete mathematics, algebraic combinatorics, coding theory, and graph theory. His favorite objects are Latin hypercubes, and one of his favorite results is the characterization of Latin hypercubes of order 4 (joint work with Vladimir Potapov).
