TITLE:
L-Convex Polyominoes: Geometrical Aspects
AUTHORS:
Khalil Tawbe, S. Mansour
KEYWORDS:
Discrete Geometry, Monotone Paths, L-Convex Polyominoes
JOURNAL NAME:
Applied Mathematics,
Vol.10 No.8,
August
5,
2019
ABSTRACT: 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.