A Steiner triple system of order v, denoted STS(v), is said to be tricyclic if it admits an automorphism whose disjoint cyclic decomposition consists of three cycles. In this thesis we give necessary and sufficient conditions for the existence of a tricyclic STS(v) when one of the cycles is of length one. In this case, the STS(v) will contain a subsystem which admits an automorphism consisting of a fixed point and a single cycle. The subsystem is said to be 1-rotational.
","abstract_html":"<p>A Steiner triple system of order <em>v</em>, denoted <em>STS</em>(<em>v</em>), is said to be <em>tricyclic</em> if it admits an automorphism whose disjoint cyclic decomposition consists of three cycles. In this thesis we give necessary and sufficient conditions for the existence of a tricyclic <em>STS</em>(<em>v</em>) when one of the cycles is of length one. In this case, the <em>STS</em>(<em>v</em>) will contain a subsystem which admits an automorphism consisting of a fixed point and a single cycle. The subsystem is said to be 1-<em>rotational</em>.</p>","abstract_has_math":false,"creators":["Tran, Quan Duc"],"institution":null,"degree_name":"MS (Master of Science)","degree_level":"Thesis - unrestricted","degree_discipline":"Mathematical Sciences","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2007,"date_issued":"2007-08-14T07:00:00Z","date_published":"2007-08-14T07:00:00Z","updated_at":"2026-07-24T02:21:19Z","subjects":["Tricyclic","Bicyclic","1-Rotational System","Steiner Triple System","Graph Automorphism","Graph Decomposition","Discrete Mathematics and Combinatorics","Mathematics","Physical Sciences and Mathematics"],"languages":[],"rights":["Copyright by the authors."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://dc.etsu.edu/etd/2102","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Tran, Quan Duc"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2007-08-14T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis - unrestricted"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS (Master of Science)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Tricyclic","Bicyclic","1-Rotational System","Steiner Triple System","Graph Automorphism","Graph Decomposition","Discrete Mathematics and Combinatorics","Mathematics","Physical Sciences and Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Copyright by the authors."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://dc.etsu.edu/context/etd/article/3463/viewcontent/TranQ080607f.pdf","https://dc.etsu.edu/etd/2102"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A Steiner triple system of order v, denoted STS(v), is said to be tricyclic if it admits an automorphism whose disjoint cyclic decomposition consists of three cycles. In this thesis we give necessary and sufficient conditions for the existence of a tricyclic STS(v) when one of the cycles is of length one. In this case, the STS(v) will contain a subsystem which admits an automorphism consisting of a fixed point and a single cycle. The subsystem is said to be 1-rotational.
"]},{"key":"dc:title","label":"Title","values":["Tricyclic Steiner Triple Systems with 1-Rotational Subsystems."]}]}],"canonical_facts":{"dc:creator":["Tran, Quan Duc"],"dc:date.issued":["2007-08-14T07:00:00Z"],"dc:description.abstract":["A Steiner triple system of order v, denoted STS(v), is said to be tricyclic if it admits an automorphism whose disjoint cyclic decomposition consists of three cycles. In this thesis we give necessary and sufficient conditions for the existence of a tricyclic STS(v) when one of the cycles is of length one. In this case, the STS(v) will contain a subsystem which admits an automorphism consisting of a fixed point and a single cycle. The subsystem is said to be 1-rotational.
"],"dc:identifier":["https://dc.etsu.edu/context/etd/article/3463/viewcontent/TranQ080607f.pdf","https://dc.etsu.edu/etd/2102"],"dc:rights":["Copyright by the authors."],"dc:subject":["Tricyclic","Bicyclic","1-Rotational System","Steiner Triple System","Graph Automorphism","Graph Decomposition","Discrete Mathematics and Combinatorics","Mathematics","Physical Sciences and Mathematics"],"dc:title":["Tricyclic Steiner Triple Systems with 1-Rotational Subsystems."],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_level":["Thesis - unrestricted"],"thesis:degree_name":["MS (Master of Science)"]},"updated_at":"2026-07-24T02:21:19Z"}