The crystallographic restriction, permutations, and Goldbach's conjecture

American Mathematical Monthly

Volumn 110, Issue 3, 2003, Pages 202-209

  Bamberg, John ^a   Cairns, Grant ^b   Kilminster, Devin ^a  

^a UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

^b LA TROBE UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037346950     PISSN: 00029890     EISSN: None     Source Type: Journal    
DOI: 10.2307/3647934     Document Type: Article

References (31)

1. G. E. Andrews, Number Theory, Dover, New York, 1994.
2. M. Aigner and G. M. Ziegler, Proofs from THE BOOK, Springer-Verlag, Berlin, 2001.
3. H. S. M. Coxeter, Regular Polytopes, Dover, New York, 1973.
4. K. Ford, The distribution of totients, Ramanujan J. 2 (1998) 67-151.
5. S. Friedland, Discrete groups of unitary isometries and balls in hyperbolic manifolds, Linear Algebra Appl. 241/243 (1996) 305-341.
6. B. Grünbaum and G. C. Shephard, Tilings and Patterns, W. H. Freeman, New York, 1987.
7. C. Hermann, Kristallographie in Räumen beliebiger Dimensionszahl. I. Die Symmetrieoperationen, Acta Cryst. 2 (1949) 139-145.
8. H. Hiller, The crystallographic restriction in higher dimensions, Acta Cryst. Sect. A 41 (1985) 541-544.
9. K. Itô, Encyclopedic Dictionary of Mathematics, MIT Press, Cambridge, 1993.
10. G. James and A. Kerber, The Representation Theory of the Symmetric Group, Addison-Wesley, Reading, MA, 1981.
11. D. Kirby, Integer matrices of finite order, Rend. Mat. 2 (1969) 403-408.
12. J. Kuzmanovich and A. Pavlichenkov, Finite groups of matrices whose entries are integers, this MONTHLY 109 (2002) 173-186.
13. n), J. Algebra 208 (1998) 630-642.
14. H. Lüneburg, Galoisfelder, Kreisteilungskörper und Schieberegisterfolgen, Bibliographisches Institut, Mannheim, 1979.
15. W. Miller, The maximum order of an element of a finite symmetric group, this MONTHLY 94 (1987) 497-506.
16. n, Acta Arith. 96 (2000) 175-203.
17. J. Parker, On Ford isometric spheres in complex hyperbolic space, Math. Proc. Cambridge Philos. Soc. 115 (1994) 501-512.
18. P. A. B. Pleasants, Quasicrystallography: some interesting new patterns, in Elementary and Analytic Theory of Numbers, H. Iwaniec, ed., Banach Center Publ. 17, Warsaw, 1985, pp. 439-461.
19. H.-E. Richert, Über Zerfällungen in ungleiche Primzahlen, Math. Z. 52 (1949) 342-343.
20. 14, Math. Comp. 70 (2001) 1745-1749.
21. A. Schinzel, Sur une conséquence de l'hypothese de Goldbach, Bǔlgar. Akad. Nauk Izv. Mat. Inst. 4 (1959) 35-38.
22. 10,000,000, Math. Comp. 63 (1994) 415-419.
23. E. Scholz, Crystallographic symmetry concepts and group theory (1850-1880), in The History of Modern Mathematics, vol. 2, D. E. Rowe and J. McCleary, eds., Academic Press, Boston, 1989, pp. 3-27.
24. R. L. E. Schwarzenberger, N-dimensional Crystallography, Pitman, Boston, 1980.
25. _, The importance of mistakes, Math. Gaz. 68 (1984) 159-172.
26. M. Senechal, Crystalline Symmetries, Adam Hilger, Bristol, 1990.
27. W. Sierpiński, Sur l'équivalence de deux hypotheses concernant les nombres premiers, Bǔlgar. Akad. Nauk Izv. Mat. Inst. 4 (1959) 3-6.
28. D. A. Suprunenko, On the order of an element of a group of integral matrices, Dokl. Akad. Nauk. BSSR 7 (1963) 221-223.
29. R. Vaidyanathaswamy, Integer-roots of the unit matrix, J. London Math. Soc. 3 (1928) 121-124.
30. _, On the possible periods of integer matrices, J. London Math. Soc. 3 (1928) 268-272.
31. H. Weyl, Symmetry, Princeton University Press, Princeton, 1989.