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Simple perfect squared squares and $ 2\times 1$ squared rectangles of order $ 25$


Author: A. J. W. Duijvestijn
Journal: Math. Comp. 62 (1994), 325-332
MSC: Primary 05B99
DOI: https://doi.org/10.1090/S0025-5718-1994-1208220-9
MathSciNet review: 1208220
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Abstract: In this note tables of all simple perfect squared squares and simple $ 2 \times 1$ perfect squared rectangles of order 25 are presented.


References [Enhancements On Off] (What's this?)

  • [1] C. J. Bouwkamp, On the dissection of rectangles into squares I, Kon. Nederl. Akad. Wetensch. 49 (1946), 1176-1188 (= Indag. Math. 8 (1946), 724-736). MR 0019310 (8:398e)
  • [2] -, On the construction of simple perfect squared squares, Kon. Nederl. Akad. Wetensch. 50 (1947), 1296-1299 (= Indag. Math. 9 (1947), 622-625). MR 0023272 (9:332g)
  • [3] -, On the dissection of rectangles into squares II, Kon. Nederl. Akad. Wetensch. 50 (1947), 58-71 (= Indag. Math. 9 (1947), 43-56). MR 0019311 (8:398f)
  • [4] -, On the dissection of rectangles into squares III, Kon. Nederl. Akad. Wetensch. 50 (1947), 72-78 (= Indag. Math. 9 (1947), 57-63).
  • [5] -, On some new simple perfect squared squares, Discrete Math. 106/107 (1992), 67-75. MR 1181898 (93i:52023)
  • [6] 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 0003040 (2:153d)
  • [7] A. J. W. Duijvestijn, Simple perfect squared squares and $ 2 \times 1$ simple perfect squared rectangles of order 21 to 24, J. Combin. Theory Ser. B 59 (1993), 26-34. MR 1234380 (94c:05017)
  • [8] -, Electronic computation of squared rectangles, Ph.D. thesis, Technological University Eindhoven, 1962. MR 0144492 (26:2036)
  • [9] -, Electronic computation of squared rectangles, Philips Research Reports 17 (1962), 523-612.
  • [10] -, Algorithmic calculation of the order of the automorphism group of a graph, Memorandum 221, Twente University of Technology, The Netherlands, 1978.
  • [11] -, A lowest order simple perfect $ 2 \times 1$ squared rectangle, J. Combin. Theory Ser. B 26 (1978), 372-374.
  • [12] -, Simple perfect squared square of lowest order, J. Combin. Theory Ser. B 25 (1978), 240-243. MR 511994 (80a:05051)
  • [13] P. J. Federico, 1978, private communication.
  • [14] -, Squaring rectangles and squares, a historical review with annotated bibliography in graph theory and related topics, Graph Theory and Related Topics, Proc. Conf. held in honour of Professor W. T. Tutte on the occasion of his sixtieth birthday, Academic Press, 1979, pp. 173-196. MR 538045 (80h:05019)
  • [15] W. T. Tutte, A theory of 3-connected graphs, Kon. Nederl. Akad. Wetensch. 64 (1961), 441-455 (= Indag. Math. 23 (1961), 441-455). MR 0140094 (25:3517)
  • [16] J. C. Wilson, A method for finding simple perfect squared squarings, Ph.D. thesis, University of Waterloo, 1967.

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1994-1208220-9
Keywords: Graph theory, squared squares, $ 2 \times 1$ squared rectangles
Article copyright: © Copyright 1994 American Mathematical Society

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