Intersection problems of Steiner triple systems
dc.contributor.advisor | Küçükçifçi Güllü, Selda | |
dc.contributor.author | Erzurumluoğlu, Aras | |
dc.date.accessioned | 2020-12-08T07:59:57Z | |
dc.date.available | 2020-12-08T07:59:57Z | |
dc.date.submitted | 2011 | |
dc.date.issued | 2018-08-06 | |
dc.identifier.uri | https://acikbilim.yok.gov.tr/handle/20.500.12812/169838 | |
dc.description.abstract | n'lik bir Steiner ¨u¸cl¨u sistemi (S¨ US(n)), (S, T ) ¸seklinde ifade edilen bir ikilidir ¨oyleki S, n elemanlı bir semboller k¨umesini, T ise S'nin 3 elemanlı bazı altk¨umelerinden(¨u¸cl¨u) olu¸san bir toplulu?gu temsil eder ve S'den se¸cilecek her eleman ikilisi T 'nintam olarak bir ¨u¸cl¨us¨unde birlikte bulunur. Bilindi?gi ¨uzere her n ? 1, 3 (mod 6)i¸cin bir S¨ US(n) vardır. Bir Steiner ¨u¸cl¨u sistemi (S, T ) i¸cin S'nin x isimli elemanınınetrafındaki ¸ci¸cek x elemanını i¸ceren t¨um ¨u¸cl¨ulerin olu¸sturdu?gu k¨ume olarak tanımlanır.E?ger T1 ? T2= k ise (S, T1) ve (S, T2) k tane ¨u¸cl¨ude kesi¸siyor denir. J(n) ve Jf (n)k¨umelerini ¸su ¸sekilde tanımlayalım:J(n) = {k ? (S, T1) ve (S, T2) ¨oyle ki T1 ? T2= k},Jf (n) = {k ? (S, T1) ve (S, T2) ¨oyle ki T1 ? T2= k + (n ? 1)/2 ve bu ¨u¸cl¨ulerin(n ? 1)/2 tanesi ortak bir ¸ci¸cek olu¸sturur}.Bu tezde n ? 1, 3 (mod 6) ¸seklindeki t¨um n'ler i¸cin J(n) ve Jf (n) k¨umelerinibelirliyoruz, ba¸ska bir ifadeyle Steiner ¨u¸cl¨u sistemlerinin kesi¸simi ve ¸ci¸cek kesi¸simiproblemlerini ¸c¨oz¨uyoruz. | |
dc.description.abstract | A Steiner triple system of order n (STS(n)) is a pair (S, T ) where S is a set ofsymbols of size n and T is a collection of 3 element subsets of S (triples) such thateach pair of distinct elements of S belongs to exactly one triple of T . It is known thata Steiner triple system exists if and only if n ? 1, 3 (mod 6). Given a Steiner triplesystem (S, T ), the flower at an element x of S is defined to be the set of all triplescontaining the element x. Two Steiner triple systems (S, T1) and (S, T2) are said tointersect in k triples if T1 ? T2= k. For all orders n ? 1, 3 (mod 6) let J(n) andJf (n) be defined asJ(n) = {k ? (S, T1) and (S, T2) such that T1 ? T2= k} andJf (n) = {k ? (S, T1) and (S, T2) such that T1?T2= k+(n?1)/2 where (n?1)/2of these common triples constitute a common flower}.This thesis is a complete survey on determining J(n) and Jf (n), i.e. on intersectionand flower intersection problems of Steiner triple systems. | en_US |
dc.language | English | |
dc.language.iso | en | |
dc.rights | info:eu-repo/semantics/openAccess | |
dc.rights | Attribution 4.0 United States | tr_TR |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
dc.subject | Matematik | tr_TR |
dc.subject | Mathematics | en_US |
dc.title | Intersection problems of Steiner triple systems | |
dc.title.alternative | Steiner üçlülerinin kesişimi problemleri | |
dc.type | masterThesis | |
dc.date.updated | 2018-08-06 | |
dc.contributor.department | Matematik Anabilim Dalı | |
dc.identifier.yokid | 407646 | |
dc.publisher.institute | Fen Bilimleri Enstitüsü | |
dc.publisher.university | KOÇ ÜNİVERSİTESİ | |
dc.identifier.thesisid | 352485 | |
dc.description.pages | 62 | |
dc.publisher.discipline | Diğer |