On minimal defining sets of full designs
| dc.contributor | Graduate Program in Mathematics. | |
| dc.contributor.advisor | Yazıcı, Emine Şule. | |
| dc.contributor.advisor | Oral, Haluk. | |
| dc.contributor.author | Demirkale, Fatih. | |
| dc.date.accessioned | 2023-03-16T11:21:35Z | |
| dc.date.available | 2023-03-16T11:21:35Z | |
| dc.date.issued | 2009. | |
| dc.description.abstract | A defining set of a t-(v; k; ̧) design is a subset of the block set of the design which is not contained in any other design with the same parameters. A defining set is said to be minimal if none of its proper subsets is a defining set. A defining set is said to be smallest if no other defining set has a smaller cardinality. A t-(v; k; ̧) design D = (V; B) is called a full design if B is the collection of all possible k-subsets of V . Every simple t-design is contained in a full design and the intersection of a defining set of a full design with a simple t-design contained in it, gives a de ning set of the corresponding t-design. With this motivation, in this thesis, the full designs are studied when the block size is 3 and several families of non-isomorphic minimal de ning sets of full designs are given. Also, it is proven that there exists some sizes in the spectrum of the full design on v elements such that the number of non-isomorphic minimal de ning sets on each of that sizes goes to infinity as . Moreover, the lower bound on the size of the defining sets of the full designs is improved with finding the size of the smallest defining sets of the full designs on 8 and 9 points. Also, all smallest defining sets of the full designs on 8 and 9 points are classified. | |
| dc.format.extent | 30cm. | |
| dc.format.pages | vii, 52 leaves; | |
| dc.identifier.other | MATH 2009 D46 | |
| dc.identifier.uri | https://digitalarchive.library.bogazici.edu.tr/handle/123456789/15242 | |
| dc.publisher | Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2009. | |
| dc.relation | Includes appendices. | |
| dc.relation | Includes appendices. | |
| dc.subject.lcsh | Set theory. | |
| dc.title | On minimal defining sets of full designs |
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