On tilings by ribbon tetrominoes
The paper is on tilings of regions using ribbon tetrominoes. A ribbon tetromino is a polyomino having 4 squares \((i,j)\) and at most one square in every diagonal \((i-j= c)\). There are 8 of these ribbon tetrominoes. If one studies tilings of simply connected regions \(T\) using these 8 objects the numbers \(a_1(T),\dots, a_8(T)\) of tetrominoes used can vary for different tilings of the same region, nevertheless certain relations between these numbers remain invariant and hence are connected to the region. The authors have found some of these relations and prove them by studying the Cayley graph of a certain group, introducing weights for the cells in this graph and calculating winding numbers connected to the closed path in the graph related to the simply connected region. The given invariants turn out to be equal to these winding numbers and hence are invariant.
scientific article; zbMATH DE number 1356443