2013/11/24 by Richard J. Mathar, Mathar, Richard J.
Materials Science · #05-04 (Secondary #05A15 #52C20 (Primary) 05B45 #Combinatorics (math.CO) #FOS: Mathematics #Quasicrystal Structures and Properties
paper · pdf · doi:10.48550/arxiv.1311.6135
openalex publication_date 2013/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The number of complete tilings of m X n floors for tiles of shape 1 X 2, 1 X 3, 1 X 4 and 2 X 3 is computed numerically for floors up to width m=9 and variable floor lengths n. Counts are obtained for two classes, for fixed tile stack orientation on one hand and for counts up to rotations and reflections on the other hand. Counts are refined by the number of points on the floor where 4 tiles meet, i.e., by the degree of violation of the requirement for Tatami tilings.