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* Hakata Workshop 2016 [#kc2dbf5e]
''～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 [#xb11a6e1]

-[[Yoshihiro Mizoguchi:http://imi.kyushu-u.ac.jp/~ym/]] (Kyushu University),~
-Hayato Waki (Kyushu University),~
-Takafumi Shibuta (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).

**Supported by [#l7bc435b]
-[[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.

**Date [#x667ba2a]
Tuesday, February 23, 2016 

**Location [#vcadf025]
-[[Academic Research and Industrial Collaboration Management office of Kyushu University ＜Momochi＞:http://imaq.kyushu-u.ac.jp/ja/imaq/access.php]]

**Program [#lfa4845b]
||~Speaker|~Title|
|10:43--10:45|>|Opening (Tetsuji Taniguchi)|
|10:45--11:30| Masashi Shinohara(Shiga University)|[[Multiply union families in &mimetex("\mathbb{N}^n"); >#cycejz44]]|
|13:00--14:30|>|[[ Poster Session (Software in Mathematics Demonstration Track in Hakata Workshop 2016):http://imi.kyushu-u.ac.jp/lasm/hakata2016/]]|
|15:10--15:55| Shuya Chiba(Kumamoto University)|[[On '''2'''-factors with '''k''' cycles in graphs >#uk3636ns]]|
|16:05--16:50| Ryuichi Harasawa(Nagasaki University)|[[A simple improvement for integer factorizations with implicit hints >#idp9ib4s]]|
|16:50--16:55|>|Closing(Yoshihiro Mizoguchi)|

**List of Poster session speakers [#h66b7b2b]
***[[Software in Mathematics Demonstration Track in Hakata Workshop 2016:http://imi.kyushu-u.ac.jp/lasm/hakata2016/]] [#h9c14217]
+山口大介 (株式会社エス・イー・エー創研) 3次元モデリング・解析システム『siren』
+松嶋聡昭 (九州大学大学院数理学府) 証明付レンガ型Wangタイリングプログラムの実装
+松尾拓哉 (九州大学大学院数理学府) 計算折り紙の定式化と折り操作の Mathematica 言語による実装
+高坂太智 (九州大学大学院数理学府) Graphの距離に関する色分けと3Dグラフィックス表示
+ (Daisuke Sakurai (RIKEN), Osamu Saeki (Kyushu University), Hamish Carr (University of Leeds), Hsiang-Yun Wu (Keio University), Takahiro Yamamoto (Kyushu Sangyo University), David Duke (University of Leeds), Kenji Ono (RIKEN), and Shigeo Takahashi (University of Aizu) Visualizing Singular Fibers – UI & Impacts –
+Daisuke Sakurai (RIKEN), Osamu Saeki (Kyushu University), Hamish Carr (University of Leeds), Hsiang-Yun Wu (Keio University), Takahiro Yamamoto (Kyushu Sangyo University), David Duke (University of Leeds), Kenji Ono (RIKEN), and Shigeo Takahashi (University of Aizu) Visualizing Singular Fibers – UI & Impacts –
+ 鈴木信之介, 上山泰史 (九州大学理学部数学科) kissing numberの上界を与える最適化問題について
+桑原雄貴 (九州大学大学院数理学府) Roc Sampler : クラスター間重複を制御するタンパク質複合体の予測アルゴリズム

**Abstract [#LINK]
***Masashi Shinohara [#cycejz44]
-Title: Multiply union families in &mimetex("\mathbb{N}^n");
-Abstract:
Let '''A''' &mimetex("\subset \mathbb{N}^n"); be an '''r'''-wise '''s'''-union family, that is, a family of sequences with '''n''' components of non-negative integers such that for any '''r''' sequences in '''A''' the total sum of the maximum of each component in those sequences is at most '''s'''.
In this talk, we determine the maximum size of '''A''' and its unique extremal configuration provided (i) '''n''' is sufficiently large for fixed '''r''' and '''s''', or (ii) '''n=r+1'''. This is a joint work with Peter Frankl and Norihide Tokushige. 


***Shuya Chiba [#uk3636ns]
-Title:On '''2'''-factors with '''k''' cycles in graphs
-Abstract:
A '''2'''-factor of a graph is a spanning collection vertex-disjoint cycles.
In [Degree conditions for '''2'''-factors, J.~Graph Theory 24 (2) (1997), 165--173],
Brandt, Chen, Faudree, Gould, Lesniak considered the degree condition
for the existence of '''2'''-factors with exactly '''k''' cycles in general graphs,
which is a generalization of Ore's classical theorem on Hamilton cycles.
In this talk, we will give some results on the degree conditions for the existence of '''2'''-factors with exactly '''k''' cycles
including every edge of a specified perfect matching in bipartite graphs,
and we will discuss about a relationship between our result and the result of Brandt et al.

***Ryuichi Harasawa [#idp9ib4s]
-Title:A simple improvement for integer factorizations with implicit hints
-Abstract:
The integer factorization is a fundamental theme of computer algebra 
and also an important topic of public key cryptography, 
especially for cryptosystems whose security relies on the infeasibility of integer factorization 
(e,g., the RSA cryptosystem). 
So far, many researchers proposed various methods for factoring integers. 
May et al. proposed a method for integer factorization with implicit hints. 
They reduced this problem to finding a shortest (or a relatively short) vector 
in the lattice obtained by implicit hints. 
In this talk, I give an improvement of May et al.'s method, 
and verify the efficiency of the improvement by computer experiments 
for various parameters.