2017 年度
第 1 回 九州大学 組合せ数学セミナー
Hakata Workshop 2017; Summer Meeting1

下記のようにセミナーを開催しますので, ご案内申し上げます。
世話人:アドバイザー :溝口 佳寛（九大 IMI） 谷口 哲至（広島工大)
島袋 修（長崎大）
田上 真（九州工大）
栗原大武（北九州高専） 千葉周也 (熊本大)坂内 英一（上海交通大学/九大数理）記
日時: 2017 年 6 月 17 日 (土) 13:43–17:35
場所:Seminar Room I (2F) in Reference Eki Higashi Building.
Higashi, Hakata-Ku, Fukuoka City, 812-0013

1-16-14 Hakata-Eki-プログラム

9:18–9:20 Opening （Tetsuji Taniguchi）
13:45–14:30 Michio Seto (National Defense Academy) (this is joint work with S. Suda)
An application of de Branges-Rovnyak space theory to graph theory
14:45–15:30 Koji Momihara (Faculty of Education, Kumamoto University)
Three-valued Gauss periods and related strongly regular Cayley graphs
15:45–16:30 Shoichi Kamada (Graduate School of Science and Technology, KumamotoUniversity)
Fractal analysis for subset sum problems
16:45–17:30 Yusuke Yamauchi ( Hiroshima Institute of Technology)
On a regularity theorem for rectangular domain
17:30–17:35 Closing （Yoshihiro Mizoguchi）
18:00– Post-meeting party

1

This conference was supported by Graduate School of Mathematics, Kyushu University, JSPS
KAKENHI(Grant-in-Aid for Scientific Research (C)) Grant Number 25400217.

Abstract
Michio Seto (National Defense Academy) (this is joint work with S. Suda)
Title: An application of de Branges-Rovnyak space theory to graph theory
Abstract: Let G1 ⊂ G2 be inclusion of two finite simple graphs. In this talk, wedeal with inner product spaces encoding the data of the defect of G1 in G2 . Ourconstruction of those inner product spaces is based on de Branges-Rovnyak space
theory in functional analysis. Further, applying the theory of quasi-orthogonal
decomposition developed by de Branges and Vasyunin-Nikolskii, some inequalities
concerning inclusion G1 ⊂ G2 are derived.
Koji Momihara (Faculty of Education, Kumamoto University)
Title: Three-valued Gauss periods and related strongly regular Cayley graphs
Abstract: It is well-known that the Cayley graph on a finite field with the set ofzeros of a nondegenerate elliptic quadratic form as its connection set is stronglyregular. Recently, Bamberg, Lee, Xiang and the speaker found new strongly regular
Cayley graphs by halving the elliptic quadric. Two-valued Gauss periods and apartition of a conic are behind this construction. In this talk, we show that theconstruction can be also done within the framework of three-valued Gauss periods.
As a consequence, we obtain two new infinite families of strongly regular Cayley
graphs.
Shoichi Kamada (Graduate School of Science and Technology, Kumamoto University)
Title: Fractal analysis for subset sum problems
Abstract: The subset sum problem has several aspects such as combinatorial aspects, number theoretic aspects, and so on. In this talk, we estimate the information
dimension for the subset sum problem, which gives the aspect of fractal analysis.
For the equation of the subset sum problem, it can be considered that the probability distribution of their coeﬃcients comes from that of fractional parts of realnumbers. We show that this enables us to estimate the information dimension.
Yusuke Yamauchi(Hiroshima Institute of Technology)
Title: On a regularity theorem for rectangular domain
Abstract: There exists a large amount of literature on a regularity theorem of
elliptic boundary value problem on smooth domains. In the field of elliptic partial
diﬀerential equation, non-smoothness of the domain has some diﬃculties, and there
are few results. In this talk, we show a regularity theorem on rectangular domain.