DOI: https://doi.org/10.15368/theses.2022.115
Available at: https://digitalcommons.calpoly.edu/theses/2650
Date of Award
12-2022
Degree Name
MS in Mathematics
Department/Program
Mathematics
College
College of Science and Mathematics
Advisor
Anthony Mendes
Advisor Department
Mathematics
Advisor College
College of Science and Mathematics
Abstract
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.