* Hakata Workshop; Winter Meeting 2019 [#c276c899]
''〜Discrete Mathematics and its Applications〜''
#br
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 [#k4943cc4]
-[[Yoshihiro Mizoguchi:http://imi.kyushu-u.ac.jp/~ym/]] (Kyushu University),~
-[[Tetsuji Taniguchi:http://researchmap.jp/tetsuzit-14/]] (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 [#mecbfbc7]
-[[Graduate School of Mathematics, Kyushu University:http://www.math.kyushu-u.ac.jp/eng/]]
-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 [#n21a9c09]
February 21, 2019
**Location [#a0e5e74f]
Kyushu University
(see https://www.kyushu-u.ac.jp/en/campus/ito/ )
**Program [#nbb7f691]
-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>#dc2ebf78]]|
|11:20-12:00| Hirotake Kurihara (National Institute of Technology, Kitakyushu College)|[[TBA>#m5bcd185]]|
|13:20-14:00| Shoichi Kamada (Kumamoto University)|[[An introduction to combinatorial $q$-fractal dimensions for a subset sum function>#c99bf778]]|
|14:10-14:50| Shoichi Tsuchiya (Senshu University)|[[Large homeomorphically irreducible trees in path-free graphs>#o74a0e9e]]|
|15:00-15:40| Asuka Takatsu (Tokyo Metropolitan University)|[[Convergence of combinatorial Ricci flows to degenerate circle patterns>#sa8ea1dc]]|
|16:00-17:30|>|[[ Poster Session (Software in Mathematics Demonstration Track in Hakata Workshop 2019):http://imi.kyushu-u.ac.jp/lasm/hakata2019/]]|
|17:30-17:35|>|Closing(Yoshihiro Mizoguchi)|
**Abstract [#u13ebdf3]
*** Asuka Takatsu [#sa8ea1dc]
-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[#dc2ebf78]
-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 [#c99bf778]
-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 [#o74a0e9e]
-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 [#m5bcd185]
-Title: TBA
-Abstract: TBA
