{"id":{"repo_id":"wfu","oai_identifier":"oai:wakespace.lib.wfu.edu:10339/82244"},"canonical_url":"https://search.dev.ndltd.org/etd/wfu/oai:wakespace.lib.wfu.edu:10339/82244","repository":{"repo_id":"wfu","name":"Wake Forest University","base_url":"https://wakespace.lib.wfu.edu/oai/request"},"display":{"title":"Crossing Number Bounds of Mosaic Knot Diagrams","abstract":"In this thesis, we tabulate some previously undocumented link mosaic diagrams. Next we prove an upper and lower bound on crossing number of certain mosaic diagrams of knots in terms of winding number for knot diagrams that make only counterclockwise turns. Next we begin drawing mosaic diagrams that have a more grid-like structure and no crossings. This grid structure of a knot is similar to a ``grid diagram\" which is equivalent to the arc presentation of a knot diagram. We generate grid diagrams using pairs of permutations from the group $((S_{n-1}\\times S_n)$. These permutations form a set of coordinate pairs that locate the position of a turn tile in the diagram.","abstract_html":"In this thesis, we tabulate some previously undocumented link mosaic diagrams. Next we prove an upper and lower bound on crossing number of certain mosaic diagrams of knots in terms of winding number for knot diagrams that make only counterclockwise turns. Next we begin drawing mosaic diagrams that have a more grid-like structure and no crossings. This grid structure of a knot is similar to a ``grid diagram&quot; which is equivalent to the arc presentation of a knot diagram. We generate grid diagrams using pairs of permutations from the group <span class=\"etd-inline-math\">((S<sub>n-1</sub>\\times S<sub>n</sub>)</span>. These permutations form a set of coordinate pairs that locate the position of a turn tile in the diagram.","abstract_has_math":true,"creators":["Roberts, Sarah Elizabeth"],"institution":"Wake Forest University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017","date_published":"2017","updated_at":"2026-07-27T22:02:11Z","subjects":["arc presentation"],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10339/82244","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Roberts, Sarah Elizabeth"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2017-06-15T08:36:13Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-06-15T08:36:13Z"]},{"key":"dc:date.issued","label":"Date","values":["2017"]},{"key":"dc:publisher","label":"Institution","values":["Wake Forest University"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["arc presentation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10339/82244"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis, we tabulate some previously undocumented link mosaic diagrams. Next we prove an upper and lower bound on crossing number of certain mosaic diagrams of knots in terms of winding number for knot diagrams that make only counterclockwise turns. Next we begin drawing mosaic diagrams that have a more grid-like structure and no crossings. This grid structure of a knot is similar to a ``grid diagram\" which is equivalent to the arc presentation of a knot diagram. We generate grid diagrams using pairs of permutations from the group $((S_{n-1}\\times S_n)$. These permutations form a set of coordinate pairs that locate the position of a turn tile in the diagram."]},{"key":"dc:title","label":"Title","values":["Crossing Number Bounds of Mosaic Knot Diagrams"]}]}],"canonical_facts":{"dc:creator":["Roberts, Sarah Elizabeth"],"dc:date.accessioned":["2017-06-15T08:36:13Z"],"dc:date.available":["2017-06-15T08:36:13Z"],"dc:date.issued":["2017"],"dc:description.abstract":["In this thesis, we tabulate some previously undocumented link mosaic diagrams. Next we prove an upper and lower bound on crossing number of certain mosaic diagrams of knots in terms of winding number for knot diagrams that make only counterclockwise turns. Next we begin drawing mosaic diagrams that have a more grid-like structure and no crossings. This grid structure of a knot is similar to a ``grid diagram\" which is equivalent to the arc presentation of a knot diagram. We generate grid diagrams using pairs of permutations from the group $((S_{n-1}\\times S_n)$. These permutations form a set of coordinate pairs that locate the position of a turn tile in the diagram."],"dc:identifier.uri":["http://hdl.handle.net/10339/82244"],"dc:language.iso":["en"],"dc:publisher":["Wake Forest University"],"dc:subject":["arc presentation"],"dc:title":["Crossing Number Bounds of Mosaic Knot Diagrams"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T22:02:11Z"}