3 papers
math.CO2025
Random Embeddings of Graphs: The Expected Number of Faces in Most Graphs is Logarithmic
Jesse Campion Loth, Kevin Halasz, Tomáš MasaÅÃk +2
A random 2-cell embedding of a connected graph in some orientable surface is obtained by choosing a random local rotation around each vertex. Under this setup, the number of fa…
math.CO2025
Moments of Colored Permutation Statistics on Conjugacy Classes
Jesse Campion Loth, Michael Levet, Kevin Liu +2
In this paper, we consider the moments of statistics on conjugacy classes of the colored permutation groups . We first show that…
math.CO2024
On the average number of cycles in conjugacy class products
Jesse Campion Loth, Amarpreet Rattan
We show that for the product of two fixed point free conjugacy classes, the average number of cycles is always very similar. Specifically, our main result is that for a randomly ch…