2016 年度
第 1 回 九州大学 組合せ数学セミナー
Hakata Workshop 20171

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） 渋田 敬史（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 2 月 23 日 (木) 9:18–17:40
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）
9:20–10:05 Masatake Hirao (Aichi Prefectural University)
QMC designs on the sphere with determinantal point processes
10:10–10:55 Hirotake Kurihara (National Institute of Technology, Kitakyushu College)
Structures of association schemes on great antipodal sets of Hermitian symmetricspaces
11:00–11:30 Tadashi Aramaki (Kyushu University)
On the zeros of certain cusp forms related to the Eisenstein series for the Fricke
groups of level 2 and 3
13:00–14:30 Poster Session
Poster Session (Software in Mathematics Demonstration Track in Hakata Workshop
2017)
15:00–15:45 Taichi Kousaka (Kyushu University)
Some properties of highly-regular graphs
15:55–16:40 Takefumi Kondo (Kagoshima University)Distortion of some finite graphs
1This conference was supported by Graduate School of Mathematics, Kyushu University, JSPS
KAKENHI(Grant-in-Aid for Scientific Research (C)) Grant Number 25400217.

16:50–17:35 Semin Oh (Pusan National University)
Demonstrations of finding finite groups all of whose symmetric fusion schemes areintegral
17:35–17:40 Closing （Yoshihiro Mizoguchi）
18:00– Post-meeting party

Poster Session
Theme: Software in Mathematics Demonstration Track
Speakers and Titles:
1. Daniel GAINA (Japan Advanced Institute of Science and Technology (JAIST))
Constructor-based Inductive Theorem Prover (CITP)
2. Semin Oh (Pusan National University) Demonstrations of finding finite groups allof whose symmetric fusion schemes are integral
3. 平野 友美 (九州大学大学院 数理学府数理学専攻) A mathematica module for 2dimensional computer graphics
4. 林 美香 (九州工業大学情報工学府) 5 頂点までの最小ユークリッド歪みについて
5. 小泉 和之 (横浜市立大学国際総合科学部) 客観的指標を用いた投手評価指標の提案
6. Ye Yuan (九州大学大学院 数理学府数理学専攻) Eﬃcient implementation of latticebased encryption schemes on multiple platforms

Abstract
Masatake Hirao (Aichi Prefectural University)
Title: QMC designs on the sphere with determinantal point processes
Abstract: The concept of a QMC(Quasi-Monte Carlo) design sequence was introduced by Brauchart et al (2014). In this talk we give a probabilistic generation ofa sequence of QMC designs by using determinantal point processes (DPPs), which
are used in a fermion model in quantum mechanics and also studied in probability
theory. We show that spherical ensembles and harmonic ensembles, which are thetypical types of DPPs on the sphere, give on average faster convergent sequences
for Sobolev space on the sphere.
Hirotake Kurihara (National Institute of Technology, Kitakyushu College)
Title: Structures of association schemes on great antipodal sets of Hermitian symmetric spaces
Abstract: For a compact Hermitian symmetric space, there is a ”good” finite subset, which is called a great antipodal set. In this talk, we will show that each great
antipodal set has a structure of an association scheme. This is a joint work with
Takayuki Okuda (Hiroshima University).
Tadashi Aramaki (Graduate school of mathematics, Kyushu University)
Title: On the zeros of certain cusp forms related to the Eisenstein series for theFricke groups of level 2 and 3.
Abstract: The location of the zeros of Eisenstein series has been considered for along time. It is known that the zeros of Eisenstein series for SL(2,Z) in the standard
fundamental domain lie on the lower arc of it. In this talk, we will present several
results for the location of the zeros of certain cusp forms related to the Eisensteinseries for the Fricke groups of level 2 and 3.
Taichi Kousaka (Graduate school of mathematics, Kyushu University)
Title: Some properties of highly-regular graphs
Abstract: Classically, highly-regular graphs have been studied as a generalization ofstrongly-regular graphs. However, highly-regular graphs can also be regarded as ageneralization of distance-regular graphs. From this view point, we study combinatorial and spectral aspects of highly-regular graphs. In this talk, as combinatorial
results, we give two constructions of highly-regular graphs and some properties ofCAM (collapsed adjacency matrix) of highly-regular graphs. Furthermore, we showthat highly-regular graphs are spectrally-regular graphs.

Takefumi Kondo (Department of Mathematics and Computer Science, Kagoshima University)
Title: Distortion of some finite graphs
Abstract: Using duality theory of semidefinite programming, Linial, London andRabinovich obtained a characterization of the least possible distortion of embeddings of finite metric spaces into Euclidean space. I will describe how this result
is applied to determine the Euclidean distortion of finite generalized polygons in ajoint work with Toshimasa Kobayashi and then discuss other methods to computethe least distortion for embeddings into CAT(0) spaces.
Semin, Oh (Pusan National University)
Title: Demonstrations of finding finite groups all of whose symmetric fusion schemes
are integral
Abstract: Let X be a finite set with size n and S = {A0 , . . . , Am } a set of (0, 1)matrices indexed by X. We say that the pair (X, S) is an association scheme (orshortly scheme) if it satisfies the following conditions:∑(i)k Ak = J, where J is the n × n all-one matrix,(ii) A0 = In , where In is the n × n identity matrix,(iii) For any A in S, the transpose matrix At of A is in S,∑(iv) For any Ai , Aj in S, Ai Aj = k pkij Ak for some constants pkij .
A scheme (X, S) is called symmetric if A = At for all A in S and integral if every
matrix in S has only integral eigenvalues. A scheme (X, T ) is called fusion schemeof (X, S) if for any matrix in T it is a sum of some matrices in S.
It is well-known that for a finite group G the association scheme of G can be obtainedby its regular action. In this talk a finite group G is called desiarable if for any
symmetric fusion scheme of the association scheme of G is integral. Observingthe one-to-one correspondence between the set of fusion schemes of the association
scheme of G and the set of Schur rings over G, we will give demonstrations of finding
finite desirable groups of small order by using GAP with COCO2p package.