BibTex RIS Kaynak Göster

ON SOME PROJECTIVE PLANES OF FINITE ORDER

Yıl 2005, Cilt: 18 Sayı: 2, 315 - 325, 13.08.2010

Atilla Akpınar

Öz

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.

Anahtar Kelimeler

Key Words: projective plane finite projective plane projective plane of order n

Kaynakça

  • 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)

Yıl 2005, Cilt: 18 Sayı: 2, 315 - 325, 13.08.2010

Atilla Akpınar

Öz

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

Anahtar Kelimeler

projektif düzlem sonlu projektif düzlem n. mertebeden projektif düzlem

Kaynakça

  • 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).
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Mathematics
Yazarlar

Atilla Akpınar

Yayımlanma Tarihi 13 Ağustos 2010
Yayımlandığı Sayı Yıl 2005 Cilt: 18 Sayı: 2

Kaynak Göster

APA Akpınar, A. (2010). ON SOME PROJECTIVE PLANES OF FINITE ORDER. Gazi University Journal of Science, 18(2), 315-325.
AMA Akpınar A. ON SOME PROJECTIVE PLANES OF FINITE ORDER. Gazi University Journal of Science. Ağustos 2010;18(2):315-325.
Chicago Akpınar, Atilla. “ON SOME PROJECTIVE PLANES OF FINITE ORDER”. Gazi University Journal of Science 18, sy. 2 (Ağustos 2010): 315-25.
EndNote Akpınar A (01 Ağustos 2010) ON SOME PROJECTIVE PLANES OF FINITE ORDER. Gazi University Journal of Science 18 2 315–325.
IEEE A. Akpınar, “ON SOME PROJECTIVE PLANES OF FINITE ORDER”, Gazi University Journal of Science, c. 18, sy. 2, ss. 315–325, 2010.
ISNAD Akpınar, Atilla. “ON SOME PROJECTIVE PLANES OF FINITE ORDER”. Gazi University Journal of Science 18/2 (Ağustos 2010), 315-325.
JAMA 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, c. 18, sy. 2, 2010, ss. 315-2.
Vancouver Akpınar A. ON SOME PROJECTIVE PLANES OF FINITE ORDER. Gazi University Journal of Science. 2010;18(2):315-2.