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Irreducible Representations From Group Actions On Trees, Charlie Liou
Irreducible Representations From Group Actions On Trees, Charlie Liou
Master's Theses
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.