Lowest order squared rectangles and squares with the largest element not on the boundary

Authors:
A. J. W. Duijvestijn and P. Leeuw

Journal:
Math. Comp. **37** (1981), 223-228

MSC:
Primary 05B45; Secondary 52A45

DOI:
https://doi.org/10.1090/S0025-5718-1981-0616375-0

MathSciNet review:
616375

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Abstract | References | Similar Articles | Additional Information

Abstract: The lowest order squared rectangles and squares with the largest element not on the boundary are presented.

**[1]**R. L. Brooks, C. A. B. Smith, A. H. Stone & W. T. Tutte, "The dissection of rectangles into squares,"*Duke Math. J.*, v. 7, 1940, pp. 312-340. MR**0003040 (2:153d)****[2]**C. J. Bouwkamp, "On the dissection of rectangles into squares,"*Proc. Acad. Sci. Amsterdam*, v. 49, 1946, pp. 1176-1188; v. 50, 1947, pp. 58-78, 1296-1299 (=*Indag. Math.*, v. 8, 1946, pp. 724-736; v. 9, 1947, pp. 43-63, 602-625). MR**0019310 (8:398e)****[3]**P. J. Federico, "Squaring rectangles and squares," A historical review with annotated bibliography in*Graph Theory and Related Topics*(Bondy and Murphy, Eds.), Academic Press, New York, 1979, pp. 173-196. MR**538045 (80h:05019)****[4]**W. T. Tutte, "A theory of 3-connected graphs,"*Proc. Acad. Sci. Amsterdam*, v. 64A, 1961 (=*Indag. Math.*, v. 23, 1961, pp. 441-455). MR**0140094 (25:3517)****[5]**A. J. W. Duijvestijn, "Electronic computation of squared rectangles,"*Philips Res. Rep.*, v. 17, 1962, pp. 523-613. MR**0144492 (26:2036)****[6]**A. J. W. Duijvestijn,*Algorithmic Identification of Graphs and Determination of the Order of the Automorphism Group of a Graph*, Memorandum 220, Twente University of Technology, Enschede, The Netherlands, 1978.**[7]**A. J. W. Duijvestijn,*Tables of Simple Squared Squares of Orders 13 Through 21 and**Rectangles of Orders*17*Through*21, Twente University of Technology, Enschede, The Netherlands, 1979.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1981-0616375-0

Keywords:
Squared rectangles,
dissection of rectangles,
tiling

Article copyright:
© Copyright 1981
American Mathematical Society