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            <front>

                <journal-meta>
                                                                <journal-id>saujs</journal-id>
            <journal-title-group>
                                                                                    <journal-title>Sakarya University Journal of Science</journal-title>
            </journal-title-group>
                                        <issn pub-type="epub">2147-835X</issn>
                                                                                            <publisher>
                    <publisher-name>Sakarya University</publisher-name>
                </publisher>
                    </journal-meta>
                <article-meta>
                                        <article-id pub-id-type="doi">10.16984/saufenbilder.962817</article-id>
                                                                <article-categories>
                                            <subj-group  xml:lang="en">
                                                            <subject>Mathematical Sciences</subject>
                                                    </subj-group>
                                            <subj-group  xml:lang="tr">
                                                            <subject>Matematik</subject>
                                                    </subj-group>
                                    </article-categories>
                                                                                                                                                        <title-group>
                                                                                                                                                            <article-title>An Existing Problem for Symmetric Design: Bruck Ryser Chowla Theorem</article-title>
                                                                                                    </title-group>
            
                                                    <contrib-group content-type="authors">
                                                                        <contrib contrib-type="author">
                                                                    <contrib-id contrib-id-type="orcid">
                                        https://orcid.org/0000-0003-4769-0830</contrib-id>
                                                                <name>
                                    <surname>Demirci Akarsu</surname>
                                    <given-names>Emek</given-names>
                                </name>
                                                                    <aff>Recep Tayyip Erdogan University</aff>
                                                            </contrib>
                                                    <contrib contrib-type="author">
                                                                    <contrib-id contrib-id-type="orcid">
                                        https://orcid.org/0000-0002-6494-6175</contrib-id>
                                                                <name>
                                    <surname>Öztürk</surname>
                                    <given-names>Safiye</given-names>
                                </name>
                                                            </contrib>
                                                                                </contrib-group>
                        
                                        <pub-date pub-type="pub" iso-8601-date="20220430">
                    <day>04</day>
                    <month>30</month>
                    <year>2022</year>
                </pub-date>
                                        <volume>26</volume>
                                        <issue>2</issue>
                                        <fpage>241</fpage>
                                        <lpage>248</lpage>
                        
                        <history>
                                    <date date-type="received" iso-8601-date="20210706">
                        <day>07</day>
                        <month>06</month>
                        <year>2021</year>
                    </date>
                                                    <date date-type="accepted" iso-8601-date="20220210">
                        <day>02</day>
                        <month>10</month>
                        <year>2022</year>
                    </date>
                            </history>
                                        <permissions>
                    <copyright-statement>Copyright © 1997, Sakarya University Journal of Science</copyright-statement>
                    <copyright-year>1997</copyright-year>
                    <copyright-holder>Sakarya University Journal of Science</copyright-holder>
                </permissions>
            
                                                                                                                        <abstract><p>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.</p></abstract>
                                                            
            
                                                                                        <kwd-group>
                                                    <kwd>Bruck Ryser Chowla Theorem</kwd>
                                                    <kwd>  Difference sets</kwd>
                                                    <kwd>  Symmetrıc designs</kwd>
                                            </kwd-group>
                            
                                                                                                                                                    </article-meta>
    </front>
    <back>
                            <ref-list>
                                    <ref id="ref1">
                        <label>1</label>
                        <mixed-citation publication-type="journal">[1]	E.S. Lander, “Symmetric Designs an Algebraic Approach,” Volume 74 of London Mathematical Society, Lecture Note Series. Cambridge University, pp. 3-40, 1983.</mixed-citation>
                    </ref>
                                    <ref id="ref2">
                        <label>2</label>
                        <mixed-citation publication-type="journal">[2]	M. Hall Jr and H.J. Ryser, “Cyclic incidence matrices,” Canadian Journal of Mathematics, vol. 3, pp. 495-502, 1951.</mixed-citation>
                    </ref>
                                    <ref id="ref3">
                        <label>3</label>
                        <mixed-citation publication-type="journal">[3]	D. Peifer, “Difference Set Transfers,” Northfield Undergraduate Mathematics Symposium, 29 Ekim, 3-4. 2013.</mixed-citation>
                    </ref>
                                    <ref id="ref4">
                        <label>4</label>
                        <mixed-citation publication-type="journal">[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.</mixed-citation>
                    </ref>
                                    <ref id="ref5">
                        <label>5</label>
                        <mixed-citation publication-type="journal">[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.</mixed-citation>
                    </ref>
                                    <ref id="ref6">
                        <label>6</label>
                        <mixed-citation publication-type="journal">[6]	M. Hall Jr, “Cyclic projective planes,” Duke Mathematical Journal, vol. 14, no. 4, pp. 1079-1090, 1947.</mixed-citation>
                    </ref>
                                    <ref id="ref7">
                        <label>7</label>
                        <mixed-citation publication-type="journal">[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.</mixed-citation>
                    </ref>
                                    <ref id="ref8">
                        <label>8</label>
                        <mixed-citation publication-type="journal">[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.</mixed-citation>
                    </ref>
                                    <ref id="ref9">
                        <label>9</label>
                        <mixed-citation publication-type="journal">[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.</mixed-citation>
                    </ref>
                                    <ref id="ref10">
                        <label>10</label>
                        <mixed-citation publication-type="journal">[10]	P. Dembowski, “Finite geometries,” Mathematics Subject Classification (1991): 51E, vol. 44, 1997.</mixed-citation>
                    </ref>
                                    <ref id="ref11">
                        <label>11</label>
                        <mixed-citation publication-type="journal">[11]	S. Chowla and H. J. Ryser, “Combinatorial problems,” Canadian Journal of Mathe matics, vol. 2, pp. 93-99, 1950.</mixed-citation>
                    </ref>
                                    <ref id="ref12">
                        <label>12</label>
                        <mixed-citation publication-type="journal">[12]	H.J. Ryser, “The existence of symmetric block designs,” Journal of Combinatorial Theory A, vol. 32, no. 1, pp. 103-105, 1982.</mixed-citation>
                    </ref>
                                    <ref id="ref13">
                        <label>13</label>
                        <mixed-citation publication-type="journal">[13]	L.D. Baumert, “Cyclic Difference Sets,” California Institute of Technology Pasadane, vol. 172, pp. 1-9, 1971.</mixed-citation>
                    </ref>
                                    <ref id="ref14">
                        <label>14</label>
                        <mixed-citation publication-type="journal">[14]	D. Raghavarao, “Constructions and Combinatorial Problems in Design of Experiments,” John Wiley, Newyork, 1971.</mixed-citation>
                    </ref>
                                    <ref id="ref15">
                        <label>15</label>
                        <mixed-citation publication-type="journal">[15]	R.E. Kibler, “A summary of noncyclic difference sets k&lt;20,” Journal of Combinatorial Theory A, vol. 25, no. 1, pp. 62-67, 1978.</mixed-citation>
                    </ref>
                                    <ref id="ref16">
                        <label>16</label>
                        <mixed-citation publication-type="journal">[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.</mixed-citation>
                    </ref>
                                    <ref id="ref17">
                        <label>17</label>
                        <mixed-citation publication-type="journal">[17]	S. Öztürk, “Fark kümelerinin varlık problemi ve Bruck Ryser Chowla Teoremi,” Yüksek Lisan Tezi, Recep Tayyip Erdoğan Üniversitesi Fen Bilimleri Enstitüsü, Rize, 2020.</mixed-citation>
                    </ref>
                                    <ref id="ref18">
                        <label>18</label>
                        <mixed-citation publication-type="journal">[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.</mixed-citation>
                    </ref>
                            </ref-list>
                    </back>
    </article>
