Simple perfect squared squares and 2×1 squared rectangles of order 26

Duijvestijn, A.

doi:10.1090/S0025-5718-96-00705-3

Simple perfect squared squares and $2\times 1$ squared rectangles of order 26
HTML articles powered by AMS MathViewer

by A. J. W. Duijvestijn PDF

Math. Comp. 65 (1996), 1359-1364 Request permission

Abstract:

In this note tables of all simple perfect squared squares and simple $2\times 1$ perfect squared rectangles of order 26 are presented.

References

A. R. Collar, On the reciprocation of certain matrices, Proc. Roy. Soc. Edinburgh 59 (1939), 195–206. MR 8, DOI 10.1017/S0370164600012281
Garrett Birkhoff and Morgan Ward, A characterization of Boolean algebras, Ann. of Math. (2) 40 (1939), 609–610. MR 9, DOI 10.2307/1968945
A. R. Collar, On the reciprocation of certain matrices, Proc. Roy. Soc. Edinburgh 59 (1939), 195–206. MR 8, DOI 10.1017/S0370164600012281
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
Bouwkamp C.J. and A.J.W. Duijvestijn, Catalogue of simple perfect squared squares of orders 21 through 25, Eut report 92-wsk-03, Eindhoven University of Technology, The Netherlands, November 1992.
—, Album of simple perfect squared squares of order 26, Eut report 94-wsk-02, Eindhoven University of Technology, The Netherlands, December 1994.
C.J.Bouwkamp, April 1993, private communication.
Adrianus Johannes Wilhelmus Duijvestijn, Electronic computation of squared rectangles, Technische Hogeschool Eindhoven, Eindhoven, 1962. Thesis; Technische Wetenschap aan de Technische Hogeschool te Eindhoven. MR 0144492
—, Electronic computation of squared rectangles, Philips Research Reports 17 (1962), 523–612.
—, Algorithmic calculation of the order of the automorphism group of a graph, Memorandum 221, Twente University of Technology, The Netherlands, 1978.
A. J. W. Duijvestijn, A lowest order simple perfect $2\times 1$ squared rectangle, J. Combin. Theory Ser. B 26 (1979), no. 3, 372–374. MR 535951, DOI 10.1016/0095-8956(79)90013-3
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
—, Simple perfect squared squares and 2 ${\times }$1 simple perfect squared rectangles of order 26, Memorandum Informatica 15, Twente University of Technology, The Netherlands, 1995.
P.J. Federico, Squaring rectangles and squares, a historical review with annotated bibliography in graph theory and related topics, Proceedings of the Conference held in honour of Professor W.T. Tutte on the occasion of his sixtieth birthday, 1979, pp. 173–196.
W. T. Tutte, A theory of $3$-connected graphs, Nederl. Akad. Wetensch. Proc. Ser. A 64 = Indag. Math. 23 (1961), 441–455. MR 0140094, DOI 10.1016/S1385-7258(61)50045-5
J.C. Wilson, A method for finding simple perfect squared squarings, Ph.D. thesis, University of Waterloo, 1967.