2 papers
math.CO2024
Centrality of star and monotone factorisations
Jesse Campion Loth, Amarpreet Rattan
A factorisation problem in the symmetric group is central if conjugate permutations always have the same number of factorisations. We give the first fully combinatorial proof of th…
math.CO2022
Expected number of faces in a random embedding of any graph is at most linear
Jesse Campion Loth, Bojan Mohar
A random 2-cell embedding of a given graph is obtained by choosing a random local rotation around every vertex. We analyze the expected number of faces of such an embedding, wh…