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ON SOME PROJECTIVE PLANES OF FINITE ORDER

Year 2005, Volume: 18 Issue: 2, 315 - 325, 13.08.2010
https://izlik.org/JA26DX37UW

Abstract

ABSTRACT

In this work, construction methods of projective planes of order 2, 3, 4, 5, 7 and 8 are examined. Informations about the obtaining of known four different planes of order 9 and non-existence of a projective plane of order 10 which is obtained according to computer based calculations are collected.

References

  • Tarry, G., Le Probleme des 36 Officiers, Compte Rendu de I’Association Française pour I’Avancement de Science Naturel, 1: 122-123 (1900).
  • Tarry, G., Le Probleme des 36 Officiers, Compte Rendu de I’Association Française pour I’Avancement de Science Naturel, 2: 170-203 (1901).
  • Bruck, R.H., Ryser H.J., “The Non-existence of Certain Finite Projective Planes”, Canadian Journal of Math., 1: 88- 93 (1949).
  • Batten, L.M., Combinatorics of Finite Geometries. Cambridge University Press, 43-44 (1986).
  • Kaya, R., Projektif Geometri. Anadolu Üniversitesi Yayınları. No:551. Eskişehir, 112-114 (1992).
  • Internet: Projective Plane of order 5. http://www.maths.monash.edu.au/~bpolster/pg5.html. (2004).
  • Beutelspacher, A., 21-6=15: A Connection Between Two Distinguished Geometries, Fachbereich Mathematik der Universitat, Saarstr. 21, D-6500 Mainz, Federal Republic of Germany, 29-40 (1986).
  • İnternet: Projective Plane of order 4. http://www.win.tue.nl/math/dw/pp/hansc/mathieu/node2.html. (2000).
  • Elkies, N., “Proof the Uniqueness of the Projective Plane of Order 5”, elkies@MATH.HARVARD.EDU. (2000).
  • Pierce, W.A., “The Impossibility of Fano’s Configuration in a Projective Plane with Eight Points Per Line”, Am. Math. Soc. Proc. ,4: 908-912 (1953).
  • Hall, M. JR., “Uniqueness of the Projective Plane with 57 Points”, Am. Math. Soc. Proc. , 4: 912-916 (1953).
  • Hall, M. JR., Correction to Uniqueness of the Projective Plane with 57 Points. Am. Math. Soc. Proc. , 5: 994-997 (1954).
  • Moufang, R., „Zur Struktur der Projektiven Geometrie der Ebene“, Math. Ann. , 105: 536-601 (1931).
  • Bose, R.C., “On the application of the properties of Galois fields to the construction of hyper-Graeco-Latin squares”, Sankhya 3: 323-338 (1938).
  • Stevenson, F. W., Projective Planes. W. H. Freeman and Company, San Francisco, 416s (1972).
  • Laywine, C.F., Mullen, G.L., Discrete Mathematics Using Latin Squares, John Wiley&Sons., NewYork. 137-140 (1998).
  • Norton, H.W., “The 7×
  • Sade, A., “An omission in Norton’s list of 7×
  • Hall, M. JR., J.D. Swıft and R.J. Walker, Uniqueness of the Projective Plane of Order Eight. Math. Tables Aids. Comput. , 10: 186-194 (1956).
  • Hughes, D.R., Piper, F.C., Projective Planes. Springer – Verlag, New York Inc, 196-201 (1973).
  • Room, T.G., Kırkpatrıck, P.B., Miniquaternion Geometry, Cambridge University Press, 176s (1971).
  • Lam, C.W.H., Kolesova, G., Thiel, L. A., “Computer Search for Finite Projective Planes of Order 9”, Discrete Mathematics, 92: 187-195 (1991).
  • Lam, C.W.H., The Search for a Finite Projective Planes of Order 10. Computer Science Department, Concordia University, American Math. Monthly, 305-318 (1991).

SONLU MERTEBELİ BAZI PROJEKTİF DÜZLEMLER ÜZERİNE (Derleme)

Year 2005, Volume: 18 Issue: 2, 315 - 325, 13.08.2010
https://izlik.org/JA26DX37UW

Abstract

Bu çalışmada 2, 3, 4, 5, 7, ve 8 mertebeli projektif düzlemlerin kuruluş metotları incelenmiş, bunların tekliklerine karşılık 9. mertebeden bilinen 4 farklı düzlemin elde edilişi ve bilgisayar araştırmalarına dayalı olarak 10. mertebeden bir projektif düzlemin yokluğu hakkındaki bilgiler derlenerek bir araya getirilmiştir

References

  • Tarry, G., Le Probleme des 36 Officiers, Compte Rendu de I’Association Française pour I’Avancement de Science Naturel, 1: 122-123 (1900).
  • Tarry, G., Le Probleme des 36 Officiers, Compte Rendu de I’Association Française pour I’Avancement de Science Naturel, 2: 170-203 (1901).
  • Bruck, R.H., Ryser H.J., “The Non-existence of Certain Finite Projective Planes”, Canadian Journal of Math., 1: 88- 93 (1949).
  • Batten, L.M., Combinatorics of Finite Geometries. Cambridge University Press, 43-44 (1986).
  • Kaya, R., Projektif Geometri. Anadolu Üniversitesi Yayınları. No:551. Eskişehir, 112-114 (1992).
  • Internet: Projective Plane of order 5. http://www.maths.monash.edu.au/~bpolster/pg5.html. (2004).
  • Beutelspacher, A., 21-6=15: A Connection Between Two Distinguished Geometries, Fachbereich Mathematik der Universitat, Saarstr. 21, D-6500 Mainz, Federal Republic of Germany, 29-40 (1986).
  • İnternet: Projective Plane of order 4. http://www.win.tue.nl/math/dw/pp/hansc/mathieu/node2.html. (2000).
  • Elkies, N., “Proof the Uniqueness of the Projective Plane of Order 5”, elkies@MATH.HARVARD.EDU. (2000).
  • Pierce, W.A., “The Impossibility of Fano’s Configuration in a Projective Plane with Eight Points Per Line”, Am. Math. Soc. Proc. ,4: 908-912 (1953).
  • Hall, M. JR., “Uniqueness of the Projective Plane with 57 Points”, Am. Math. Soc. Proc. , 4: 912-916 (1953).
  • Hall, M. JR., Correction to Uniqueness of the Projective Plane with 57 Points. Am. Math. Soc. Proc. , 5: 994-997 (1954).
  • Moufang, R., „Zur Struktur der Projektiven Geometrie der Ebene“, Math. Ann. , 105: 536-601 (1931).
  • Bose, R.C., “On the application of the properties of Galois fields to the construction of hyper-Graeco-Latin squares”, Sankhya 3: 323-338 (1938).
  • Stevenson, F. W., Projective Planes. W. H. Freeman and Company, San Francisco, 416s (1972).
  • Laywine, C.F., Mullen, G.L., Discrete Mathematics Using Latin Squares, John Wiley&Sons., NewYork. 137-140 (1998).
  • Norton, H.W., “The 7×
  • Sade, A., “An omission in Norton’s list of 7×
  • Hall, M. JR., J.D. Swıft and R.J. Walker, Uniqueness of the Projective Plane of Order Eight. Math. Tables Aids. Comput. , 10: 186-194 (1956).
  • Hughes, D.R., Piper, F.C., Projective Planes. Springer – Verlag, New York Inc, 196-201 (1973).
  • Room, T.G., Kırkpatrıck, P.B., Miniquaternion Geometry, Cambridge University Press, 176s (1971).
  • Lam, C.W.H., Kolesova, G., Thiel, L. A., “Computer Search for Finite Projective Planes of Order 9”, Discrete Mathematics, 92: 187-195 (1991).
  • Lam, C.W.H., The Search for a Finite Projective Planes of Order 10. Computer Science Department, Concordia University, American Math. Monthly, 305-318 (1991).
There are 23 citations in total.

Details

Primary Language English
Authors

Atilla Akpınar

Publication Date August 13, 2010
IZ https://izlik.org/JA26DX37UW
Published in Issue Year 2005 Volume: 18 Issue: 2

Cite

APA Akpınar, A. (2010). ON SOME PROJECTIVE PLANES OF FINITE ORDER. Gazi University Journal of Science, 18(2), 315-325. https://izlik.org/JA26DX37UW
AMA 1.Akpınar A. ON SOME PROJECTIVE PLANES OF FINITE ORDER. Gazi University Journal of Science. 2010;18(2):315-325. https://izlik.org/JA26DX37UW
Chicago Akpınar, Atilla. 2010. “ON SOME PROJECTIVE PLANES OF FINITE ORDER”. Gazi University Journal of Science 18 (2): 315-25. https://izlik.org/JA26DX37UW.
EndNote Akpınar A (August 1, 2010) ON SOME PROJECTIVE PLANES OF FINITE ORDER. Gazi University Journal of Science 18 2 315–325.
IEEE [1]A. Akpınar, “ON SOME PROJECTIVE PLANES OF FINITE ORDER”, Gazi University Journal of Science, vol. 18, no. 2, pp. 315–325, Aug. 2010, [Online]. Available: https://izlik.org/JA26DX37UW
ISNAD Akpınar, Atilla. “ON SOME PROJECTIVE PLANES OF FINITE ORDER”. Gazi University Journal of Science 18/2 (August 1, 2010): 315-325. https://izlik.org/JA26DX37UW.
JAMA 1.Akpınar A. ON SOME PROJECTIVE PLANES OF FINITE ORDER. Gazi University Journal of Science. 2010;18:315–325.
MLA Akpınar, Atilla. “ON SOME PROJECTIVE PLANES OF FINITE ORDER”. Gazi University Journal of Science, vol. 18, no. 2, Aug. 2010, pp. 315-2, https://izlik.org/JA26DX37UW.
Vancouver 1.Atilla Akpınar. ON SOME PROJECTIVE PLANES OF FINITE ORDER. Gazi University Journal of Science [Internet]. 2010 Aug. 1;18(2):315-2. Available from: https://izlik.org/JA26DX37UW