3 papers
math.CO2025
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.CO2025
Combinatorial enumeration of lattice paths by flaws with respect to a linear boundary of rational slope
Federico Firoozi, Jonathan Jedwab, Amarpreet Rattan
Let be fixed positive coprime integers. For a positive integer , write for the set of lattice paths from the startpoint to the endpoint with ste…
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…