We study the representations of the symmetric group $S_n$ found by acting on
labeled graphs and trees with $n$ vertices. Our main results provide
combinatorial interpretations that give the number of times the irreducible
representations associated with the integer partitions $(n)$ and $(1^n)$ appear
in the representations. We describe a new sign
reversing involution with fixed points that provide a combinatorial
interpretation for the number of times the irreducible associated with the
integer partition $(n-1, 1)$ appears in the representations.
| Identifer | oai:union.ndltd.org:CALPOLY/oai:digitalcommons.calpoly.edu:theses-4194 |
| Date | 01 December 2022 |
| Creators | Liou, Charlie |
| Publisher | DigitalCommons@CalPoly |
| Source Sets | California Polytechnic State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Master's Theses |
Page generated in 0.0062 seconds