On Partitioning Colored Points

P. Kirchberger proved that, for a finite subset $X$ of $\mathbb{R}^{d}$ such that each point in $X$ is painted with one of two colors, if every $d+2$ or fewer points in $X$ can be separated along the colors, then all the points in $X$ can be separated along the colors. In this paper, we show a more colorful theorem

2分割による分離概念と関連する幾何問題について

京都大学0048新制・課程博士博士(人間・環境学)甲第16951号人博第594号新制||人||142(附属図書館)23||人博||594(吉田南総合図書館)29626京都大学大学院人間・環境学研究科共生人間学専攻(主査)准教授 立木 秀樹, 教授 髙﨑 金久, 准教授 伊藤 大雄学位規則第4条第1項該当Doctor of Human and Environmental StudiesKyoto UniversityDA

Extracting Co-Occurrence Relations from ZDDs

A zero-suppressed binary decision diagram (ZDD) is a graph representation suitable for handling sparse set families. Given a ZDD representing a set family, we present an efficient algorithm to discover a hidden structure, called a co-occurrence relation, on the ground set. This computation can be done in time complexity that is related not to the number of sets, but to some feature values of the ZDD. We furthermore introduce a conditional co-occurrence relation and present an extraction algorithm, which enables us to discover further structural information

On separating families of bipartitions

AbstractWe focus on families of bipartitions, i.e. set partitions consisting of at most two components. A family of bipartitions is a separating family for a set if every two elements in the set are separated by some bipartition. In this paper we enumerate separating families of arbitrary size. We furthermore enumerate inclusion-wise minimal separating families of minimum and maximum sizes

Hyphalion sagamiense, a new species of Clausidiidae (Copepoda: Poecilostomatoida) associated with a vesicomyid bivalve from the Hatsushima cold-seep site in Sagami Bay, Japan

Volume: 105Start Page: 102End Page: 11