Indecomposability: polyominoes and polyomino tilings

Abstract

When we were preparing our earlier article [1], we thought to look back to see what else had appeared in the Gazette on the subject of polyominoes. A polyomino is a finite collection of cells in the square grid with connected interior - so it is insufficient that cells be connected only corner to corner. Some authors require polyominoes to have a simply connected interior, that is, to be without holes, as was appropriate, for example, in [1] for stack polyominoes. The classic text on polyominoes is Solomon Golomb's engaging book [2], first published in 1965, now supplemented at an even more accessible level by [3].