<i>L</i>-Convex Polyominoes: Geometrical Aspects

• 作者: Khalil Tawbe S. Mansour
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Discrete Geometry MONOTONE PATHS L-Convex POLYOMINOES
• 年，卷（期）: 2019,（8）
• 页码范围: 646-658
• 页数: 13页
• 分类号: O1

摘要

A polyomino P is called L-convex if for every two cells there exists a monotone path included in P with at most one change of direction. This paper is a theoretical step for the reconstruction of all L-convex polyominoes by using the geometrical paths. First we investigate the geometrical properties of all subclasses of non-directed L-convex polyominoes by giving nine geometries that characterize all non-directed L-convex polyominoes. Finally, we study the subclasses of directed L-convex polyominoes and we give necessary and sufficient conditions for polyominoes to be L-convex.