Dissections of $p : q$ rectangles
HTML articles powered by AMS MathViewer
- by Charles H. Jepsen PDF
- Math. Comp. 65 (1996), 771-778 Request permission
Abstract:
We determine all simple perfect dissections of $p:q$ rectangles into at most twelve $p:q$ 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
- A. R. Collar, On the reciprocation of certain matrices, Proc. Roy. Soc. Edinburgh 59 (1939), 195–206. MR 8, DOI 10.1017/S0370164600012281
- C. J. Bouwkamp, On some new simple perfect squared squares, Discrete Math. 106/107 (1992), 67–75. A collection of contributions in honour of Jack van Lint. MR 1181898, DOI 10.1016/0012-365X(92)90531-J
- Leonard Eugene Dickson, New First Course in the Theory of Equations, John Wiley & Sons, Inc., New York, 1939. MR 0000002
- A. J. W. Duijvestijn, Simple perfect squared square of lowest order, J. Combin. Theory Ser. B 25 (1978), no. 2, 240–243. MR 511994, DOI 10.1016/0095-8956(78)90041-2
- A. J. W. Duijvestijn, Simple perfect squared squares and $2\times 1$ squared rectangles of orders $21$ and $24$, J. Combin. Theory Ser. B 59 (1993), no. 1, 26–34. MR 1234380, DOI 10.1006/jctb.1993.1051
- A. J. W. Duijvestijn, Simple perfect squared squares and $2\times 1$ squared rectangles of order $25$, Math. Comp. 62 (1994), no. 205, 325–332. MR 1208220, DOI 10.1090/S0025-5718-1994-1208220-9
- C. H. Jepsen, Dissections into $1:2$ rectangles, Discrete Math. (to appear).
- Carsten Müller, Perfekte Rechteckzerlegung, Elem. Math. 45 (1990), no. 4, 98–106 (German). MR 1059549
Additional Information
- Charles H. Jepsen
- Affiliation: Department of Mathematics, Grinnell College, Grinnell, Iowa 50112
- Email: jepsen@math.grin.edu
- Received by editor(s): January 11, 1995
- © Copyright 1996 American Mathematical Society
- Journal: Math. Comp. 65 (1996), 771-778
- MSC (1991): Primary 05B99, 68R10
- DOI: https://doi.org/10.1090/S0025-5718-96-00711-9
- MathSciNet review: 1333316