Published in Journal of Combinatorial Theory, Series A 83 (1998), no. 1, p. 158.

TILING A SQUARE WITH EIGHT CONGRUENT POLYOMINOES

Michael Reid

Department of Mathematics, Brown University

October 7, 1997

The problem of finding polyominoes that tile rectangles has attracted a lot of attention; see [1] for an overview, and [2, 3] for more recent results. Several general families of such polyominoes are known, but sporadic examples seem to be scarce. Marshall [2, Fig. 9] gives a polyomino of rectangular order 8, and asks if it can be generalized to a family of rectifiable polyominoes.

Here we show one way to generalize Marshall’s construction, which yields an infinite family of polyominoes of rectangular order 8. Marshall’s construction is the first square in Figure 1.

Figure 1. Infinite family of polyominoes of rectangular order 8.

References

1. Solomon W. Golomb, Tiling rectangles with polyominoes, The Mathematical Intelligencer 18 (1996), no. 2, 38–47. MR 97f:05047

2. William Rex Marshall, Packing rectangles with congruent polyominoes, Journal of Combinatorial Theory, Series A 77 (1997), no. 2, 181–192. MR 98e:05026

3. Michael Reid, Tiling rectangles and half strips with congruent polyominoes, Journal of Combinatorial Theory, Series A 80 (1997), no. 1, 106–123. MR 98i:05046

Old address:  Current address:
Michael Reid  Michael Reid
Department of Mathematics  Department of Mathematics
Box 1917  University of Central Florida
Brown University  Orlando, FL 32816
Providence, RI 02912  U.S.A.

   U.S.A.  reid@cflmath.com

   reid@math.brown.edu

Typeset by AMS-TEX