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Dissections of rectangles
Author(s):
Charles
H.
Jepsen.
Journal:
Math. Comp.
65
(1996),
771-778.
MSC (1991):
Primary 05B99, 68R10
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Abstract:
We determine all simple perfect dissections of rectangles into at most twelve rectangular elements. A computer search shows there are only eight such dissections, two of order 10, three of order 11, and three of order 12.
References:
- 1.
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- 2.
- ------, On some new simple perfect squared squares, Discrete Math. 106/107 (1992), 67--75. MR 93i:52023
- 3.
- R. L. Brooks, C. A. B. Smith, A. H. Stone, and W. T. Tutte, The dissection of rectangles into squares, Duke Math. J. 7 (1940), 312--340. MR 2:153d
- 4.
- A. J. W. Duijvestijn, Simple perfect square of lowest order, J. Combin. Theory Ser. B 25 (1978), 240--243. MR 80a:05051
- 5.
- ------, Simple perfect squared squares and
squared rectangles of orders 21 to 24, J. Combin. Theory Ser. B 59 (1993), 26--34. MR 94c:05017 - 6.
- ------, Simple perfect squared squares and
squared rectangles of order 25, Math. Comp. 62 (1994), 325--332. MR 94c:05023 - 7.
- C. H. Jepsen, Dissections into
rectangles, Discrete Math. (to appear). - 8.
- Carsten Müller, Perfekte Rechteckzerlegung, El. Math.
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Additional Information:
Charles
H.
Jepsen
Affiliation:
Department of Mathematics, Grinnell College, Grinnell, Iowa 50112
Email:
jepsen@math.grin.edu
DOI:
10.1090/S0025-5718-96-00711-9
PII:
S 0025-5718(96)00711-9
Keywords:
Simple perfect dissection,
$c$-net,
$p$-net
Received by editor(s):
January 11, 1995
Copyright of article:
Copyright
1996,
American Mathematical Society
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