The 81st KPPY Combinatorics Seminar
Organized by S.Bang, M.Hirasaka, T.Jensen, J.Koolen and M.Siggers February 21, 2017
Date
February 21, 2017 Place
Building 607, Room 208,
Department of Mathematics in Pusan National University Program
11:00–11:50, Seungjai Lee (NIMS)
A survey on zeta functions of groups and rings 13:40–14:30, Eun Kyoung Cho (PNU)
On finite groups which induces only commutative proper Schur rings 14:40–15:30, Jongyook Park (KIAS)
On 2-walk-regular graphs
16:00–16:50, Sejeong Bang (Yeungnam University) Determination of geometric distance-regular graphs 17:00–17:50, Mitsugu Hirasaka (PNU)
On finite metric spaces with some properties on distances and triangles 18:30–20:30, Banquet
1
Name: Seungjai Lee (NIMS)
Title: A survey on zeta functions of groups and rings
Abstract: Over the last few decades, zeta functions of groups and rings have become important tools in various areas of asymptotic group and ring theory. In this talk, I will introduce their definitions with brief history of their developments and their applications. I shall also present recent discoveries, and discuss further problems to solve.
Name:Eun Kyoung Cho (PNU)
Title:On finite groups which induces only commutative proper Schur rings Abstract: Consider a group ringC[G] and a partition
P ={D0 ={e}, D1,· · · , Dd}of G. LetD∗i ={g−1 |g∈Di} and ¯Di is the sum of all the elements ofDi for all i∈ {0,1,· · ·, d}. Then a subalgebra of C[G] generated by ¯D0,D¯1,· · · ,D¯d is called a Schur ring over Gand is denoted byG= (G;P). In this talk, we classify a groupGsuch that every proper Schur ring over it is commutative.
References
[1] A. Misseldine,Counting Schur Rings over Cyclic Groups, arXiv:1508.03757v1 [math.RA]
[2] D.S. Dumit, R. M. Foote,Abstract Algebra, Wiley, 2004 [3] G. A. Miller, H.C. Moreno, Non-abelian groups in which every
subgroup is abelian, Trans. Amer. Math. Soc. 4 (1903), 398–404.
[4] T. W. Hungerfold,Algebra, volume 73 of Graduate Texts in Mathematics, (1980)
[5] W. Shiu,Algebraic Structure of Schur Rings, Chinese J. Math.
(Taiwan, R.O.C.) 21 (1993), 55–71.
[6] W. Shiu,Schur rings over dihedral groups of order 2p, (1989).
University of Hong Kong, Pokfulam, Hon Kong SAR.
Name: Jongyook Park (KIAS) Title: On 2-walk-regular graphs
Abstract: A t-walk-regular graph is a common generalization of
distance-regular graphs on the one hand and t-arc-transitive graphs on the other hand. We focus on the case wheret= 2 because s-walk-regular graphs aret-walk-regular ifs≥tand many properties of distance-regular graphs can be generalized to 2-walk-regular graphs. In this talk, we first introduce some known results that hold for 2-walk-regular graphs but are not true in general for 1-walk-regular graphs. And then we will generalize a known result of distance-regular graphs to the class of 2-walk-regular graphs. (This is joint work with Jack Koolen and Zhi Qiao.)
Name: Sejeong Bang (Yeungnam University)
Title: Determination of geometric distance-regular graphs
Abstract: A non-complete distance-regular graph is calledgeometric if there exists a setC of Delsarte cliques such that each edge lies in exactly one clique in C. In this talk we study how to determine given
distance-regular graphs with large valency are geometric or not.
Name: Mitsugu Hirasaka (Pusan National University)
Title: On finite metric spaces characterized by distances and triangles Abstract: Let (X, d) be a finite metric space with |X|=n. For a positive integerkwe define Ak(X) to be the quotient set of all k-subsets ofX by isometry, and we denote |Ak(X)|byak. The sequence (a1, a2, . . . , an) is called theisometric sequence of (X, d). In this talk we aim to characterize finite metric spaces witha2=a3 = 4.
