The Tilling Using Ω-Class of Nested Abacus

Abstract

This study applies a class of Abacus diagrams, referred to as the Ω-class of Nested Abacus (N.C.A), to the problem of tiling within finite regions. An algorithm was developed using mapping notation to represent the movement of subsets containing multiple β-positions and empty β-positions. The new class was embedded to facilitate tiling in a finite rectangular region. Furthermore, a theoretical model was formulated to describe the tiling process in finite regions based on the proposed Nested Abacus approach.