Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2022, , 241 - 248, 30.04.2022
https://doi.org/10.16984/saufenbilder.962817

Öz

Kaynakça

  • [1] E.S. Lander, “Symmetric Designs an Algebraic Approach,” Volume 74 of London Mathematical Society, Lecture Note Series. Cambridge University, pp. 3-40, 1983.
  • [2] M. Hall Jr and H.J. Ryser, “Cyclic incidence matrices,” Canadian Journal of Mathematics, vol. 3, pp. 495-502, 1951.
  • [3] D. Peifer, “Difference Set Transfers,” Northfield Undergraduate Mathematics Symposium, 29 Ekim, 3-4. 2013.
  • [4] J. Singer, “A theorem in finite projective geometry and some applications to number theory,” Transactions of the American Mathematical Society, vol. 43, no. 3, pp. 377-385, 1938.
  • [5] R.C. Bose and K.R. Nair, “Partially balanced incomplete block designs,” Sankhya: The Indian Journal of Statistics, vol. 4, no. 3, pp. 337-372, 1939.
  • [6] M. Hall Jr, “Cyclic projective planes,” Duke Mathematical Journal, vol. 14, no. 4, pp. 1079-1090, 1947.
  • [7] F.W. Levi, “Groups in which the commutator operation satisfies certain algebraic conditions,” The Journal of the Indian Mathematical Society, vol. 6, pp. 87-97. 1942.
  • [8] R.H. Bruck and H.J. Ryser, “The non existence of certain finite projective planes,” Canadian Journal of Mathematics, vol. 1, no. 1, pp. 88-93, 1949.
  • [9] M.P. Schützenberger, “A Nonexistence Theorem for Infinite family of symmetrical block designs,” Annals of Human Genetics, vol. 14, no. 1, pp. 286-287, 1949.
  • [10] P. Dembowski, “Finite geometries,” Mathematics Subject Classification (1991): 51E, vol. 44, 1997.
  • [11] S. Chowla and H. J. Ryser, “Combinatorial problems,” Canadian Journal of Mathe matics, vol. 2, pp. 93-99, 1950.
  • [12] H.J. Ryser, “The existence of symmetric block designs,” Journal of Combinatorial Theory A, vol. 32, no. 1, pp. 103-105, 1982.
  • [13] L.D. Baumert, “Cyclic Difference Sets,” California Institute of Technology Pasadane, vol. 172, pp. 1-9, 1971.
  • [14] D. Raghavarao, “Constructions and Combinatorial Problems in Design of Experiments,” John Wiley, Newyork, 1971.
  • [15] R.E. Kibler, “A summary of noncyclic difference sets k<20,” Journal of Combinatorial Theory A, vol. 25, no. 1, pp. 62-67, 1978.
  • [16] P. J. Cameron and J. H. Lint, “Desings, Graps, Codes and their Links www.maa.org/programs/maa-awards/writing-awards/the-search-for-finite-projective-plane-of-order-10,” Cambridge University Press, 1991.
  • [17] S. Öztürk, “Fark kümelerinin varlık problemi ve Bruck Ryser Chowla Teoremi,” Yüksek Lisan Tezi, Recep Tayyip Erdoğan Üniversitesi Fen Bilimleri Enstitüsü, Rize, 2020.
  • [18] E. Demirci Akarsu, “Almost Difference Sets and Cyclotomy,” in Academic Studies in Science and Mathematics. Izmir, Turkey: Platanus Duvar Publishing, ch. 10, pp. 143–159, 2021.

An Existing Problem for Symmetric Design: Bruck Ryser Chowla Theorem

Yıl 2022, , 241 - 248, 30.04.2022
https://doi.org/10.16984/saufenbilder.962817

Öz

Symetric designs are interesting objects of combinatorics, and have some relations with coding theory, difference sets, geometry and finite group theory. They have applications on statistics and design experiments. In the present paper we study an existing problem for symmetric design due to Bruck, Ryser and Chowla and write an algorithm by using their theorem called BRC Theorem.

Kaynakça

  • [1] E.S. Lander, “Symmetric Designs an Algebraic Approach,” Volume 74 of London Mathematical Society, Lecture Note Series. Cambridge University, pp. 3-40, 1983.
  • [2] M. Hall Jr and H.J. Ryser, “Cyclic incidence matrices,” Canadian Journal of Mathematics, vol. 3, pp. 495-502, 1951.
  • [3] D. Peifer, “Difference Set Transfers,” Northfield Undergraduate Mathematics Symposium, 29 Ekim, 3-4. 2013.
  • [4] J. Singer, “A theorem in finite projective geometry and some applications to number theory,” Transactions of the American Mathematical Society, vol. 43, no. 3, pp. 377-385, 1938.
  • [5] R.C. Bose and K.R. Nair, “Partially balanced incomplete block designs,” Sankhya: The Indian Journal of Statistics, vol. 4, no. 3, pp. 337-372, 1939.
  • [6] M. Hall Jr, “Cyclic projective planes,” Duke Mathematical Journal, vol. 14, no. 4, pp. 1079-1090, 1947.
  • [7] F.W. Levi, “Groups in which the commutator operation satisfies certain algebraic conditions,” The Journal of the Indian Mathematical Society, vol. 6, pp. 87-97. 1942.
  • [8] R.H. Bruck and H.J. Ryser, “The non existence of certain finite projective planes,” Canadian Journal of Mathematics, vol. 1, no. 1, pp. 88-93, 1949.
  • [9] M.P. Schützenberger, “A Nonexistence Theorem for Infinite family of symmetrical block designs,” Annals of Human Genetics, vol. 14, no. 1, pp. 286-287, 1949.
  • [10] P. Dembowski, “Finite geometries,” Mathematics Subject Classification (1991): 51E, vol. 44, 1997.
  • [11] S. Chowla and H. J. Ryser, “Combinatorial problems,” Canadian Journal of Mathe matics, vol. 2, pp. 93-99, 1950.
  • [12] H.J. Ryser, “The existence of symmetric block designs,” Journal of Combinatorial Theory A, vol. 32, no. 1, pp. 103-105, 1982.
  • [13] L.D. Baumert, “Cyclic Difference Sets,” California Institute of Technology Pasadane, vol. 172, pp. 1-9, 1971.
  • [14] D. Raghavarao, “Constructions and Combinatorial Problems in Design of Experiments,” John Wiley, Newyork, 1971.
  • [15] R.E. Kibler, “A summary of noncyclic difference sets k<20,” Journal of Combinatorial Theory A, vol. 25, no. 1, pp. 62-67, 1978.
  • [16] P. J. Cameron and J. H. Lint, “Desings, Graps, Codes and their Links www.maa.org/programs/maa-awards/writing-awards/the-search-for-finite-projective-plane-of-order-10,” Cambridge University Press, 1991.
  • [17] S. Öztürk, “Fark kümelerinin varlık problemi ve Bruck Ryser Chowla Teoremi,” Yüksek Lisan Tezi, Recep Tayyip Erdoğan Üniversitesi Fen Bilimleri Enstitüsü, Rize, 2020.
  • [18] E. Demirci Akarsu, “Almost Difference Sets and Cyclotomy,” in Academic Studies in Science and Mathematics. Izmir, Turkey: Platanus Duvar Publishing, ch. 10, pp. 143–159, 2021.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Araştırma Makalesi
Yazarlar

Emek Demirci Akarsu 0000-0003-4769-0830

Safiye Öztürk 0000-0002-6494-6175

Yayımlanma Tarihi 30 Nisan 2022
Gönderilme Tarihi 6 Temmuz 2021
Kabul Tarihi 10 Şubat 2022
Yayımlandığı Sayı Yıl 2022

Kaynak Göster

APA Demirci Akarsu, E., & Öztürk, S. (2022). An Existing Problem for Symmetric Design: Bruck Ryser Chowla Theorem. Sakarya University Journal of Science, 26(2), 241-248. https://doi.org/10.16984/saufenbilder.962817
AMA Demirci Akarsu E, Öztürk S. An Existing Problem for Symmetric Design: Bruck Ryser Chowla Theorem. SAUJS. Nisan 2022;26(2):241-248. doi:10.16984/saufenbilder.962817
Chicago Demirci Akarsu, Emek, ve Safiye Öztürk. “An Existing Problem for Symmetric Design: Bruck Ryser Chowla Theorem”. Sakarya University Journal of Science 26, sy. 2 (Nisan 2022): 241-48. https://doi.org/10.16984/saufenbilder.962817.
EndNote Demirci Akarsu E, Öztürk S (01 Nisan 2022) An Existing Problem for Symmetric Design: Bruck Ryser Chowla Theorem. Sakarya University Journal of Science 26 2 241–248.
IEEE E. Demirci Akarsu ve S. Öztürk, “An Existing Problem for Symmetric Design: Bruck Ryser Chowla Theorem”, SAUJS, c. 26, sy. 2, ss. 241–248, 2022, doi: 10.16984/saufenbilder.962817.
ISNAD Demirci Akarsu, Emek - Öztürk, Safiye. “An Existing Problem for Symmetric Design: Bruck Ryser Chowla Theorem”. Sakarya University Journal of Science 26/2 (Nisan 2022), 241-248. https://doi.org/10.16984/saufenbilder.962817.
JAMA Demirci Akarsu E, Öztürk S. An Existing Problem for Symmetric Design: Bruck Ryser Chowla Theorem. SAUJS. 2022;26:241–248.
MLA Demirci Akarsu, Emek ve Safiye Öztürk. “An Existing Problem for Symmetric Design: Bruck Ryser Chowla Theorem”. Sakarya University Journal of Science, c. 26, sy. 2, 2022, ss. 241-8, doi:10.16984/saufenbilder.962817.
Vancouver Demirci Akarsu E, Öztürk S. An Existing Problem for Symmetric Design: Bruck Ryser Chowla Theorem. SAUJS. 2022;26(2):241-8.

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Fark kümelerinin varlık problemi
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https://doi.org/10.17714/gumusfenbil.1105985

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