# Hakata Workshop;Winter Meeting 2019

Last-modified: 2019-02-18 (月) 20:41:33 (30d)

Top / Hakata Workshop;Winter Meeting 2019

## Hakata Workshop; Winter Meeting 2019 †

**〜Discrete Mathematics and its Applications〜**

Our purpose of this meeting is giving an opportunity to make a speech and to communicate with researchers who study various fields not only Combinatorics.

Further information is available from the organizers below.

### Organizers †

- Yoshihiro Mizoguchi (Kyushu University),
- Tetsuji Taniguchi (Hiroshima Institute of Technology),
- Osamu Shimabukuro (Nagasaki University),
- Makoto Tagami (Kyushu Institute of Technology),
- Hirotake Kurihara (Kitakyushu National College of Technology),
- Shuya Chiba (Kumamoto University),
- Tsuyoshi Miezaki (University of the Ryukyus).

### Supported by †

- Graduate School of Mathematics, Kyushu University
- JSPS KAKENHI(Grant-in-Aid for Scientific Research (C)) Grant Number 25400217.
- JSPS KAKENHI(Grant-in-Aid for Scientific Research (C)) Grant Number 17K05346

### Date †

February 21, 2019

### Location †

Kyushu University W1-D-413 (see https://www.kyushu-u.ac.jp/en/campus/ito/ )

### Program †

- Thursday, February 21

Speaker | Title | |
---|---|---|

10:27-10:30 | Opening (Tetsuji Taniguchi) | |

10:30-11:10 | Makoto Tagami (Kyushu Institute of Technology) | Harmonic Index t-design in Hamming Schemes |

11:20-12:00 | Hirotake Kurihara (National Institute of Technology, Kitakyushu College) | Lagrangian subalgebras and rooted tree graphs |

13:20-14:00 | Shoichi Kamada (Kumamoto University) | An introduction to combinatorial $q$-fractal dimensions for a subset sum function |

14:10-14:50 | Shoichi Tsuchiya (Senshu University) | Large homeomorphically irreducible trees in path-free graphs |

15:00-15:40 | Asuka Takatsu (Tokyo Metropolitan University) | Convergence of combinatorial Ricci flows to degenerate circle patterns |

16:00-17:30 | Poster Session (Software in Mathematics Demonstration Track in Hakata Workshop 2019) | |

17:30-17:35 | Closing(Yoshihiro Mizoguchi) |

### List of Poster session speakers †

#### Software in Mathematics Demonstration Track in Hakata Workshop 2019 †

- 矢澤明喜子（信州大学大学院総合理工学研究科） 行列式点過程を用いた条件付きspanning treeの個数の数え上げについて
- Semin Oh（Pusan National University） Finding Minimal UFA-free Graphs
- Xiaolu Xu（Dalian University of Technology） An R package for identifying driver genes and driver pathways
- 森山 卓（九州大学マス・フォア・インダストリ研究所） 非負値行列因子分解を用いた多峰性関数の分解についての検討
- 原田 海音（琉球大学 教育学部） 一般化正多面体の仮想的対称性
- 富安 亮子（九州大学 IMI） Powder indexing software CONOGRAPH
- 久米 美沙紀（琉球大学 教育学部 ） 高種数タット多項式の計算プログラム
- 栗原寛明（九州大学大学院数理学府） トポロジーの手法を用いた点群のクラスタリング手法
- Ye Yuan（Graduate School of Mathematics, Kyushu University） Experimental Studies in Implementations of Post-Quantum Key Exchange Protocols using HTML5 Multithreading Approach
- 高橋康（九州大学大学院数理学府） Groebner基底計算を用いた同種写像問題求解法の提案と実装

### Abstract †

#### Asuka Takatsu †

- Title: Convergence of combinatorial Ricci flows to degenerate circle patterns
- Abstract: On a connected, oriented, closed surface, a circle pattern metric determines a geometric structure (Riemannian metric of constant curvature) from a topological structure (weighted triangulation). A criterion for the existence of a circle pattern metric on a surface of nonpositive Euler characteristic was first proved by Thurston. Chow–Luo gave the algorithm, so-called the combinatorial Ricci flow, to find circle pattern metrics. Chow–Luo raised some questions about the combinatorial Ricci flow, one of which is to investigate the combinatorial Ricci flow when a circle pattern metric does not exist. In my talk, I address this question.

#### Makoto Tagami †

- Title: Harmonic Index t-design in Hamming Schemes
- Abstract: The notion of harmonic index (or simply HI) spherical design was introduced as a finite set on a sphere in the form extending the notion of usual spherical designs by Bannai-Okuda-T (2015). They studied about a Fisher type inequality and construction for HI spherical design and argued about the non-existence of tight HI spherical designs. While Zhu-Bannai-Bannai-Ikuta-Kim(2017) reintroduced the notion of HI $t$-design in symmetric association schemes and they studied about HI $t$-designs in binary Hamming schemes. In this talk, we will study them in Hamming scheme H(n,q) for arbitrary q following BOT and ZBBIK .

#### Shoichi Kamada †

- Title: An introduction to combinatorial $q$-fractal dimensions for a subset sum function
- Abstract: The subset sum problem, which is NP-hard, can be replaced by finding an inverse image of a subset sum function. Many of cryptosystems based on the subset sum problem have been broken since the hardness of this problem depends on its density. In this talk, we introduce the notion of a combinatorial $q$-fractal dimension for a subset sum function. This notion is a combinatorial analogue of the generalized dimension in multi-fractal analysis and includes the density of the subset sum problem. We give a lower bound for a combinatorial $q$-fractal dimension. The method is combinatorial rather than algebraic.

#### Shoichi Tsuchiya †

- Title: Large homeomorphically irreducible trees in path-free graphs
- Abstract: A connected graph G is said to be P_{n}-free if G contains no path of order n as an induced subgraph. A subgraph of G is a homeomorphically irreducible tree (or a HIT) if it is a tree with no vertices of degree two. If a HIT of G is a spanning subgraph of G, it is called a homeomorphically irreducible spanning tree (or a HIST). When n=4 or 5, connected P_{n}-free graphs with a HIST were characterized. From these results, we can guarantee a large HIT in connected P_{n}-free graphs when n=4 or 5. In this talk, we consider a problem whether connected path-free graphs G contain a HIT with linear order of |G|.

#### Hirotake Kurihara †

- Title: Lagrangian subalgebras and rooted tree graphs
- Abstract: The study of Lagrangian submanifolds in Kähler manifolds is a fruitful area in differential geometry of submanifolds. If an ambient space has a structure of Hermitian symmetric space, then "homogeneous" Lagrangian submanifolds are obtained from certain Lie subalgebras, which is called Lagrangian subalgebras. In my talk, I will show constructions of Lagrangian subalgebras of Lie algebras derived from certain Hermitian symmetric spaces of noncompact type, obtained from rooted tree graphs. This is a joint work with Takahiro Hashinaga (National Institute of Technology, Kitakyushu College).