{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/118942"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/118942","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"A Novel Insertion Algorithm","abstract":"Through the definition of a new insertion algorithm this paper seeks to provide an alternative to the existing bijections between permutations and certain kinds of tableaux. We will define two versions of each algorithm covered, both the existing ones and the novel one. These different constructions will include one using a lot of small intermediate steps and one which directly creates the tableaux from the permutation. After showing that these are equivalent, we will briefly discuss the results of pattern avoidance on tableau shape.","abstract_html":"Through the definition of a new insertion algorithm this paper seeks to provide an alternative to the existing bijections between permutations and certain kinds of tableaux. We will define two versions of each algorithm covered, both the existing ones and the novel one. These different constructions will include one using a lot of small intermediate steps and one which directly creates the tableaux from the permutation. After showing that these are equivalent, we will briefly discuss the results of pattern avoidance on tableau shape.","abstract_has_math":false,"creators":["Quinlan, Isis"],"institution":"Virginia Tech","degree_name":"Doctor of Philosophy","degree_level":"doctoral","degree_discipline":"Mathematics","degree_department":"Mathematics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Shimozono, Mark M."],"committee_members":["Orr, Daniel D.","Loehr, Nicholas A.","Mihalcea, Constantin Leonardo"],"year":2024,"date_issued":"2024-05-09","date_published":"2024-05-09","updated_at":"2026-07-22T22:20:11Z","subjects":["algebraic combinatorics"],"languages":["en"],"rights":["Creative Commons Attribution 4.0 International"],"rights_urls":["http://creativecommons.org/licenses/by/4.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:40607"],"render_values":[{"text":"vt_gsexam:40607","href":null,"code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/10919/118942","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Shimozono, Mark M."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Orr, Daniel D.","Loehr, Nicholas A.","Mihalcea, Constantin Leonardo"]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Quinlan, Isis"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2024-05-10T08:00:15Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2024-05-10T08:00:15Z"]},{"key":"dc:date.issued","label":"Date","values":["2024-05-09"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["algebraic combinatorics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Creative Commons Attribution 4.0 International"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://creativecommons.org/licenses/by/4.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:40607"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10919/118942"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Through the definition of a new insertion algorithm this paper seeks to provide an alternative to the existing bijections between permutations and certain kinds of tableaux. We will define two versions of each algorithm covered, both the existing ones and the novel one. These different constructions will include one using a lot of small intermediate steps and one which directly creates the tableaux from the permutation. After showing that these are equivalent, we will briefly discuss the results of pattern avoidance on tableau shape."]},{"key":"dc:description.abstractgeneral","label":"General Abstract","values":["Building up tableaux from permutations can be a helpful way to get information about that permutation without having to check by hand. Different methods of building tableaux will tell us different types of information about the permutation. For that reason, we are defining a new method of building tableaux so that we can extract useful information from the permutations used."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Doctor of Philosophy"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["ETD"]},{"key":"dc:title","label":"Title","values":["A Novel Insertion Algorithm"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Shimozono, Mark M."],"dc:contributor.committeemember":["Orr, Daniel D.","Loehr, Nicholas A.","Mihalcea, Constantin Leonardo"],"dc:contributor.department":["Mathematics"],"dc:creator":["Quinlan, Isis"],"dc:date.accessioned":["2024-05-10T08:00:15Z"],"dc:date.available":["2024-05-10T08:00:15Z"],"dc:date.issued":["2024-05-09"],"dc:description.abstract":["Through the definition of a new insertion algorithm this paper seeks to provide an alternative to the existing bijections between permutations and certain kinds of tableaux. We will define two versions of each algorithm covered, both the existing ones and the novel one. These different constructions will include one using a lot of small intermediate steps and one which directly creates the tableaux from the permutation. After showing that these are equivalent, we will briefly discuss the results of pattern avoidance on tableau shape."],"dc:description.abstractgeneral":["Building up tableaux from permutations can be a helpful way to get information about that permutation without having to check by hand. Different methods of building tableaux will tell us different types of information about the permutation. For that reason, we are defining a new method of building tableaux so that we can extract useful information from the permutations used."],"dc:description.degree":["Doctor of Philosophy"],"dc:format.medium":["ETD"],"dc:identifier.other":["vt_gsexam:40607"],"dc:identifier.uri":["https://hdl.handle.net/10919/118942"],"dc:language.iso":["en"],"dc:publisher":["Virginia Tech"],"dc:rights":["Creative Commons Attribution 4.0 International"],"dc:rights.uri":["http://creativecommons.org/licenses/by/4.0/"],"dc:subject":["algebraic combinatorics"],"dc:title":["A Novel Insertion Algorithm"],"dc:type":["Dissertation"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Doctor of Philosophy"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:20:11Z"}