An octomino of high order
The order of an \(n\)-omino is the smallest value of \(k\) such that \(k\) copies of it can be used to tile a rectangle of area \(kn\). Previous results on tiling rectangles with polyominoes have been obtained in this journal by the first author [ibid. 51, No. 1, 125-126 and 127-128 (1989; Zbl 0715.05013 and Zbl 0715.05014)], the second author [ibid. 51, No. 1, 117-124 (1989; Zbl 0723.05041)] and \textit{D. A. Klarner} [J. Comb. Theory 7, No. 2, 107-115 (1969; Zbl 0174.041)], who found an octomino of order 24. In this paper the first author has found an octomino such that 312 copies of it tile a \(26\times 96\) rectangle. The last author has found another octomino that can tile a \(32\times \infty\) half-strip. It is not known at present whether there is a rectangle that can be tiled by this octomino.
scientific article; zbMATH DE number 740292