{"id":{"repo_id":"calpoly","oai_identifier":"oai:digitalcommons.calpoly.edu:theses-4194"},"canonical_url":"https://search.dev.ndltd.org/etd/calpoly/oai:digitalcommons.calpoly.edu:theses-4194","repository":{"repo_id":"calpoly","name":"Cal Poly","base_url":"https://digitalcommons.calpoly.edu/do/oai/"},"display":{"title":"Irreducible Representations from Group Actions on Trees","abstract":"<p>We study the representations of the symmetric group $S_n$ found by acting on</p> <p>labeled graphs and trees with $n$ vertices. Our main results provide</p> <p>combinatorial interpretations that give the number of times the irreducible</p> <p>representations associated with the integer partitions $(n)$ and $(1^n)$ appear</p> <p>in the representations. We describe a new sign</p> <p>reversing involution with fixed points that provide a combinatorial</p> <p>interpretation for the number of times the irreducible associated with the</p> <p>integer partition $(n-1, 1)$ appears in the representations.</p>","abstract_html":"&lt;p&gt;We study the representations of the symmetric group <span class=\"etd-inline-math\">S<sub>n</sub></span> found by acting on&lt;/p&gt; &lt;p&gt;labeled graphs and trees with $n$ vertices. Our main results provide&lt;/p&gt; &lt;p&gt;combinatorial interpretations that give the number of times the irreducible&lt;/p&gt; &lt;p&gt;representations associated with the integer partitions $(n)$ and <span class=\"etd-inline-math\">(1<sup>n</sup>)</span> appear&lt;/p&gt; &lt;p&gt;in the representations. We describe a new sign&lt;/p&gt; &lt;p&gt;reversing involution with fixed points that provide a combinatorial&lt;/p&gt; &lt;p&gt;interpretation for the number of times the irreducible associated with the&lt;/p&gt; &lt;p&gt;integer partition $(n-1, 1)$ appears in the representations.&lt;/p&gt;","abstract_has_math":true,"creators":["Liou, Charlie"],"institution":null,"degree_name":"MS in Mathematics","degree_level":null,"degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Anthony Mendes","Mathematics","College of Science and Mathematics"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-12-01T08:00:00Z","date_published":"2022-12-01T08:00:00Z","updated_at":"2026-07-24T01:32:55Z","subjects":["Discrete Mathematics and Combinatorics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["10.15368/theses.2022.115"],"render_values":[{"text":"10.15368/theses.2022.115","href":"https://doi.org/10.15368/theses.2022.115","code":true}]}]},"links":{"outbound_url":"https://digitalcommons.calpoly.edu/theses/2650","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Anthony Mendes","Mathematics","College of Science and Mathematics"]},{"key":"dc:creator","label":"Author","values":["Liou, Charlie"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2022-12-09T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS in Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Discrete Mathematics and Combinatorics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.calpoly.edu/theses/2650","10.15368/theses.2022.115"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["<p>We study the representations of the symmetric group $S_n$ found by acting on</p> <p>labeled graphs and trees with $n$ vertices. Our main results provide</p> <p>combinatorial interpretations that give the number of times the irreducible</p> <p>representations associated with the integer partitions $(n)$ and $(1^n)$ appear</p> <p>in the representations. We describe a new sign</p> <p>reversing involution with fixed points that provide a combinatorial</p> <p>interpretation for the number of times the irreducible associated with the</p> <p>integer partition $(n-1, 1)$ appears in the representations.</p>"]},{"key":"dc:title","label":"Title","values":["Irreducible Representations from Group Actions on Trees"]}]}],"canonical_facts":{"dc:contributor":["Anthony Mendes","Mathematics","College of Science and Mathematics"],"dc:creator":["Liou, Charlie"],"dc:date.available":["2022-12-09T08:00:00Z"],"dc:description.abstract":["<p>We study the representations of the symmetric group $S_n$ found by acting on</p> <p>labeled graphs and trees with $n$ vertices. Our main results provide</p> <p>combinatorial interpretations that give the number of times the irreducible</p> <p>representations associated with the integer partitions $(n)$ and $(1^n)$ appear</p> <p>in the representations. We describe a new sign</p> <p>reversing involution with fixed points that provide a combinatorial</p> <p>interpretation for the number of times the irreducible associated with the</p> <p>integer partition $(n-1, 1)$ appears in the representations.</p>"],"dc:identifier":["https://digitalcommons.calpoly.edu/theses/2650","10.15368/theses.2022.115"],"dc:subject":["Discrete Mathematics and Combinatorics"],"dc:title":["Irreducible Representations from Group Actions on Trees"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_name":["MS in Mathematics"]},"updated_at":"2026-07-24T01:32:55Z"}