Research Article
BibTex RIS Cite
Year 2022, , 241 - 248, 30.04.2022
https://doi.org/10.16984/saufenbilder.962817

Abstract

References

  • [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

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

Abstract

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.

References

  • [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.
There are 18 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Emek Demirci Akarsu 0000-0003-4769-0830

Safiye Öztürk 0000-0002-6494-6175

Publication Date April 30, 2022
Submission Date July 6, 2021
Acceptance Date February 10, 2022
Published in Issue Year 2022

Cite

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. April 2022;26(2):241-248. doi:10.16984/saufenbilder.962817
Chicago Demirci Akarsu, Emek, and Safiye Öztürk. “An Existing Problem for Symmetric Design: Bruck Ryser Chowla Theorem”. Sakarya University Journal of Science 26, no. 2 (April 2022): 241-48. https://doi.org/10.16984/saufenbilder.962817.
EndNote Demirci Akarsu E, Öztürk S (April 1, 2022) An Existing Problem for Symmetric Design: Bruck Ryser Chowla Theorem. Sakarya University Journal of Science 26 2 241–248.
IEEE E. Demirci Akarsu and S. Öztürk, “An Existing Problem for Symmetric Design: Bruck Ryser Chowla Theorem”, SAUJS, vol. 26, no. 2, pp. 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 (April 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 and Safiye Öztürk. “An Existing Problem for Symmetric Design: Bruck Ryser Chowla Theorem”. Sakarya University Journal of Science, vol. 26, no. 2, 2022, pp. 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.

Cited By

Fark kümelerinin varlık problemi
Gümüşhane Üniversitesi Fen Bilimleri Enstitüsü Dergisi
https://doi.org/10.17714/gumusfenbil.1105985

30930 This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.