Around Rédei's theorem

Discrete Mathematics

Volumn 208-209, Issue , 1999, Pages 557-575

  Szonyi, Tamás ^a  

^a EÖTVÖS LORÁND UNIVERSITY   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041995420     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-365X(99)00097-7     Document Type: Article

References (54)

1. N. Alon, Tools from higher algebra, in: R.L. Graham, M. Grötschel, L. Lovász (Eds.), Handbook of Combinatorics (Chapter 32), North-Holland, Amsterdam, 1995.
2. S. Ball, On the size of a triple blocking set in PG(2,q), European J. Combin. 17 (1996) 427-435.
3. S. Ball, A. Blokhuis, On the size of a double blocking set in PG(2, q), Finite Fields Appl. 2 (1996) 125-137.
4. Á. Bereczky, Fixed-point free p-elements in transitive permutation groups, J. London Math. Soc. 27 (1995) 447-452.
5. 2 + n lines, J. Geom. 15 (1980) 175-181.
6. 2) with square differences, Indag. Math. 46 (1984) 369-372.
7. A. Blokhuis, On the size of a blocking set in PG(2, p), Combinatorica 14 (1994) 111-114.
8. A. Blokhuis, Blocking sets in Desarguesian planes, in: D. Miklós, V.T. Sós, T. Szonyi (Eds.), Combinatorics: Paul Erdos is Eighty, vol. 2, János Bolyai Mathematical Society, Budapest, 1996, pp. 133-154.
9. A. Blokhuis, S. Ball, A.E. Brouwer, L. Storme, T. Szonyi, On the number of slopes of the graph of a function defined on a finite field, J. Combin. Theory Ser. A. 86 (1999) 187-196.
10. A. Blokhuis, A.E. Brouwer, T. Szonyi, The number of directions determined by a function f on a finite field, J. Comb. Theory Ser. A. 70 (1995) 349-353.
11. A. Blokhuis, R. Pellikaan, T. Szonyi, Blocking sets of almost Rédei type, J. Combin. Theory Ser. A. 78 (1997) 141-150.
12. A. Blokhuis, J.J. Seidel, Remark on Wielandt's visibility theorem, Linear Algebra Appl. 71 (1985) 29-30.
13. A. Blokhuis, L. Storme, T. Szonyi, Multiple blocking sets and Baer subplanes, J. London Math. Soc., to appear.
14. A. Blokhuis, O. Polverino, private communication.
15. A. Borevich, I.R. Shafarevich, Algebraic Theory of Numbers, Academic Press, New York, 1966.
16. G. Bacsó, E. Boros, V. Gurvich, F. Maffray, M. Preissmann, On minimally imperfect graphs with circular symmetry, J. Graph Theory 29 (1998) 209-225.
17. A.A. Bruen, Baer subplanes and blocking sets, Bull. Amer. Math. Soc. 76 (1970) 342-344.
18. A.A. Bruen, Blocking sets in finite projective planes, SIAM J. Appl. Math. 21 (1971) 380-392.
19. A. Bruen, Arcs and multiple blocking sets, in: Proceedings of the Conference on Finite Geometries, INdAM, Rome, Italy, 1983, Symposia Math., vol. 23, Academic Press, New York, 1986, pp. 15-29.
20. A.A. Bruen, Nuclei of sets of q + 1 points in PG(2, q) and blocking sets of Rédei type, J. Combin. Theory A 55 (1990) 130-132.
21. A.A. Bruen, J.C. Fisher, On the method of Jamison, Des. Codes Cryptography 1 (1991) 199-205.
22. A.A. Bruen, J.A. Thas, Blocking sets, Geom. Dedicata 6 (1977) 193-203.
23. N.G. de Bruijn, On number systems, Nieuw Archief voor Wiskunde 3 (1956) 15-17.
24. D. de Caen, D.A. Gregory, I.G. Hughes, D.L. Kreher, Near-factors of finite groups, Ars. Combin. 29 (1990) 53-63.
25. P.J. Cameron, Four lectures on projective geometry, in: C.A. Baker, L.M. Batten (Eds.), Finite Geometries, Lecture Notes in Pure and Applied Mathematics, vol. 103, Marcel Dekker, New York, Basel, 1985, pp. 27-65.
26. L. Carlitz, A note on exponential sums, Acta Sci. Math. (Szeged) 21 (1960) 135-143.
27. K.A. Corrádi, S. Szabó, On a theorem of László Rédei, Mat. Lapok 34 (1983-87) 25-39 (in Hungarian).
28. R.S. Coulter, R.W. Matthews, Planar functions and planes of Lenz-Barlotti class II, Des. Codes Cryptography 10 (1997) 167-184.
29. 2, Math. Zeit. 103 (1968) 239-258.
30. p and a theorem of W. Burnside, Bayreuther Math. Schriften 40 (1992) 7-19.
31. R.J. Evans, J. Greene, H. Niederreiter, Linearized polynomials and permutation polynomials on finite fields, Michigan Math. J. 39 (1992) 405-413.
32. A. Gács, A remark on blocking sets of almost Rédei type, J. Geom. 60 (1997) 65-73.
33. A. Gács, On the number of directions determined by a point set in AG(2, p), Discrete Math. 208/209 (this Vol.) (1999) 299-309.
34. A. Gács, T. Szonyi, Double blocking sets and Baer-subplanes, unpublished manuscript, 1995.
35. A. Gács, P. Sziklai, T. Szonyi, Two remarks on blocking sets and nuclei in planes of prime order, Des. Codes Cryptography 10 (1997) 29-39.
36. D. Gluck, A note on permutation polynomials and finite geometries, Discrete Math. 80 (1990) 97-100.
37. U. Heim, Blockierende Mengen in endlichen projektiven Räumen, Mitt. Math. Sem. Univ. Giessen 226 (1996) 1-82.
38. Y. Hiramine, A conjecture on affine planes of prime order, J. Combin. Theory A 52 (1989) 44-50.
39. J.W.P. Hirschfeld, Projective Geometries over Finite Fields, Oxford University Press, Oxford, 1979.
40. 2, J. Geometry 30 (1987) 49-68.
41. L. Lovász, A. Schrijver, Remarks on a theorem of Rédei, Studia Scient. Math. Hungar. 16 (1981) 449-454.
42. U. Ott, Group association schemes and Schur rings, Le Matematiche (Catania) XLVII (1992) 281-294.
43. L. Rédei, Lückenhafte Polynome über endlichen Körpern, Birkhäuser Verlag, Basel (1970) (English translation: Lacunary polynomials over finite fields, North-Holland, Amsterdam, 1973).
44. L. Rédei, Lückenhafte Polynome über endlichen Körpern, Birkhäuser Verlag, Basel (1970) (English translation: Lacunary polynomials over finite fields, North-Holland, Amsterdam, 1973).
45. L. Rédei, Die neue Theorie der endlichen abelschen Gruppen und Verallgemeinerung des Hauptsatzes von Hajós, Acta Math. Hungar. 18 (1967) 329-373.
46. L. Rónyai, T. Szonyi, Planar functions over finite fields, Combinatorica 9 (1989) 315-320.
47. S. Szabó, private communication
48. S. Szabó, Space filling cube systems, (in Hungarian), Mat. Lapok 32 (1984) 49-73.
49. S. Szabó, On decomposing finite abelian groups, Acta Math. Acad. Sci. Hungar. 36 (1980) 105-141.
50. K.-O. Stöhr, J.F. Voloch, Weierstrass points and curves over finite fields, Proc. London Math. Soc. 52 (3) (1986) 1-19.
51. T. Szonyi, Combinatorial problems for abelian groups arising from geometry, Per. Polytechnica 19 (1991) 91-100.
52. T. Szonyi, On the number of directions determined by a set of points in an affine Galois plane, J. Combin. Theory Ser. A 74 (1996) 141-146.
53. T. Szonyi, Blocking sets in desarguesian affine and projective planes, Finite Fields Appl. 3 (1997) 187-202.
54. E. Wittmann, Einfacher Beweis des Hauptsatzes von Hajós-Rédei für elementare Gruppen von Primzahlquadratordnung, Acta Math. Acad. Sci. Hungar. 20 (1969) 227-230.