2015 年度
第 2 回 九州大学 組合せ数学セミナー
Hakata Workshop 20161

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） 脇 隼人 (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: 2016 年 2 月 23 日 (火) 10:43–16:55
場所:Academic Research and Industrial Collaboration Management oﬃce of Kyushu University ＜ Momochi ＞ URL: http://comb.math.kyushu-u.ac.jp/

プログラム

10:43–10:45 Opening （Tetsuji Taniguchi）
10:45–11:30 Masashi Shinohara(Shiga University)
Multiply union families in Nn
13:00–14:30 Poster Session
Poster Session (Software in Mathematics Demonstration Track in Hakata Workshop2016)
15:10–15:55 Shuya Chiba(Kumamoto University)
On 2-factors with k cycles in graphs
16:05–16:50 Ryuichi Harasawa(Nagasaki University)
A simple improvement for integer factorizations with implicit hints
16:50–16:55 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.

Poster Session
Theme: Software in Mathematics Demonstration TrackSpeakers and Titles:
1. 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』
2. 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
3. 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
4. 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
5. 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), andShigeo Takahashi (University of Aizu) Visualizing Singular Fibers - UI & Impacts6. 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
7. 桑原雄貴 (九州大学大学院数理学府) RocSampler : 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
Masashi Shinohara(Shiga University)
Title: Multiply union families in Nn
Abstract: Let A ⊂ Nn be an r-wise s-union family, that is, a family of sequenceswith n components of non-negative integers such that for any r sequences in A thetotal 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(Kumamoto University)
Title: On 2-factors with k cycles in graphs Abstract: A 2-factor of a graph isa 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 theexistence of 2-factors with exactly k cycles including every edge of a specified perfectmatching in bipartite graphs, and we will discuss about a relationship between our
result and the result of Brandt et al.
Ryuichi Harasawa(Nagasaki University)
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 thisproblem to finding a shortest (or a relatively short) vector in the lattice obtained byimplicit 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.