{"id":{"repo_id":"siu-theses","oai_identifier":"oai:opensiuc.lib.siu.edu:dissertations-2427"},"canonical_url":"https://search.dev.ndltd.org/etd/siu-theses/oai:opensiuc.lib.siu.edu:dissertations-2427","repository":{"repo_id":"siu-theses","name":"Southern Illinois University","base_url":"https://opensiuc.lib.siu.edu/do/oai/"},"display":{"title":"Double-Change Covering Designs with Block Size k = 4","abstract":"A double-change covering design (dccd) is an ordered set of blocks with block size k is an ordered collection of b blocks, B = {B1,B2, · · · ,Bb}, each an unordered subset of k distinct elements from [v] = {1, 2, · · · , v}, which obey: (1) each block differs from the previous block by two elements, and, (2) every unordered pair of [v] appears in at least one block. The object is to minimize b for a fixed v and k. Tight designs are those in which each pair is covered exactly once. We present constructions of tight dccd’s for arbitrary v when k = 2 and minimal constructions for v <= 20 when k = 4. A general, but not minimal, method is presented to construct circular dccd for arbitrary v when k = 4.","abstract_html":"A double-change covering design (dccd) is an ordered set of blocks with block size k is an ordered collection of b blocks, B = {B1,B2, · · · ,Bb}, each an unordered subset of k distinct elements from [v] = {1, 2, · · · , v}, which obey: (1) each block differs from the previous block by two elements, and, (2) every unordered pair of [v] appears in at least one block. The object is to minimize b for a fixed v and k. Tight designs are those in which each pair is covered exactly once. We present constructions of tight dccd’s for arbitrary v when k = 2 and minimal constructions for v &lt;= 20 when k = 4. A general, but not minimal, method is presented to construct circular dccd for arbitrary v when k = 4.","abstract_has_math":false,"creators":["Gamachchige, Nirosh Tharaka Sandakelum Gangoda"],"institution":null,"degree_name":"Doctor of Philosophy","degree_level":"Campus Only Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["McSorley, John"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017-08-01T07:00:00Z","date_published":"2017-08-01T07:00:00Z","updated_at":"2026-07-24T04:35:23Z","subjects":["circular designs","combinatorial designs","covering designs","double-change","tight designs"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://opensiuc.lib.siu.edu/dissertations/1423","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["McSorley, John"]},{"key":"dc:creator","label":"Author","values":["Gamachchige, Nirosh Tharaka Sandakelum Gangoda"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Campus Only Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["circular designs","combinatorial designs","covering designs","double-change","tight designs"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://opensiuc.lib.siu.edu/dissertations/1423"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A double-change covering design (dccd) is an ordered set of blocks with block size k is an ordered collection of b blocks, B = {B1,B2, · · · ,Bb}, each an unordered subset of k distinct elements from [v] = {1, 2, · · · , v}, which obey: (1) each block differs from the previous block by two elements, and, (2) every unordered pair of [v] appears in at least one block. The object is to minimize b for a fixed v and k. Tight designs are those in which each pair is covered exactly once. We present constructions of tight dccd’s for arbitrary v when k = 2 and minimal constructions for v <= 20 when k = 4. A general, but not minimal, method is presented to construct circular dccd for arbitrary v when k = 4."]},{"key":"dc:title","label":"Title","values":["Double-Change Covering Designs with Block Size k = 4"]}]}],"canonical_facts":{"dc:contributor":["McSorley, John"],"dc:creator":["Gamachchige, Nirosh Tharaka Sandakelum Gangoda"],"dc:description.abstract":["A double-change covering design (dccd) is an ordered set of blocks with block size k is an ordered collection of b blocks, B = {B1,B2, · · · ,Bb}, each an unordered subset of k distinct elements from [v] = {1, 2, · · · , v}, which obey: (1) each block differs from the previous block by two elements, and, (2) every unordered pair of [v] appears in at least one block. The object is to minimize b for a fixed v and k. Tight designs are those in which each pair is covered exactly once. We present constructions of tight dccd’s for arbitrary v when k = 2 and minimal constructions for v <= 20 when k = 4. A general, but not minimal, method is presented to construct circular dccd for arbitrary v when k = 4."],"dc:identifier":["https://opensiuc.lib.siu.edu/dissertations/1423"],"dc:subject":["circular designs","combinatorial designs","covering designs","double-change","tight designs"],"dc:title":["Double-Change Covering Designs with Block Size k = 4"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Campus Only Dissertation"],"thesis:degree_name":["Doctor of Philosophy"]},"updated_at":"2026-07-24T04:35:23Z"}