Tiling design - Colegiul National C. Negruzzi (Iași - Roumanie)

Titre du sujet
Tiling design
Établissement
Colegiul National C. Negruzzi (Iași - Roumanie)
Année
2018-2019
Résumé
Our work focuses on counting the number of different tiling designs that can be obtained on a or a lattice, using three types of tiles: 1x1 squares, dominos and L-shaped trominos. To this end, we have derived appropriate reccurence relations, based on which we were able to find the number of all possible tiling designs. For all items in the research proposal, we have provided detailed combinatorial solutions, with suggestive graphical representations. Similar work can be done for more general lattices, such as chessboards or non-rectangular shaped lattices.