Perfect squared squares, orders 21 to 24 (and some of orders 25 to 27)

The number of simple and compound perfect squared squares of various orders is known to be as follows:

Order Simple Compound
<21 0 0
21 1 [Duijvestijn, 1978] 0
22 8 [Duijvestijn, 1993] 0
23 12 [Duijvestijn, 1993] 0
24 26 [Duijvestijn, 1993] 1 [Willcocks, 1951; Duijvestijn, Federico and Leeuw, 1982]
25 160 [Duijvestijn, 1994] >=1
26 441 [Duijvestijn, 1996] >=2
27 >=227 [Bouwkamp, 1998] >=2

Here, the compound perfect squared squares obtained by changing the orientation of the squared rectangle inside the squared square are not counted as different. If I have a list of the squares' Bouwkamp codes, there is a link to it above.

Thanks to Stuart Anderson for providing squared squares of order 25 and 27.

Bibliography

[Bouwkamp, 1998]: Simple perfect squared squares of order 27,EUT Report-WSK, 98-1 (Eindhoven University of Technology technical report), 1998.

[Duijvestijn, 1978]: Simple perfect squared square of lowest order, J. Combinatorial Theory Series B, 25, #2 (1978), 240-243.

[Dujivestijn, 1993]: Simple perfect squared squares and 2x1 squared rectangles of orders 21 and 24, J. Combinatorial Theory Series B, 59, (1993), 26-34.

[Dujivestijn, 1994]: Simple perfect squared squares and 2x1 squared rectangles of order 25, Mathematics of Computation, 62, (1994), 325-332.

[Dujivestijn, 1996]: Simple perfect squared squares and 2x1 squared rectangles of order 26, Mathematics of Computation, 65, (1996), 1359-1364.

[Duijvestijn, Federico and Leeuw, 1982]: Compound perfect squares, American Mathematical Monthly, 89, (1982), 15-32.

[Willcocks, 1951]: A note on some perfect squared squares, Canadian J. Math., 3, (1951), 304-308.

David Moews ( dmoews@fastmail.fm )

Last updated 20-IX-2004