Amarpreet Rattan

activity

20052024

most citedUpper bound on the characters of the symmetric groups for balanced Young diagrams and a generalized Frobenius formula

18 citations · 36 across the 17 of their papers we have counts for

collaborators

17 papers

math.CO2024

Combinatorial enumeration of lattice paths by flaws with respect to a linear boundary of rational slope

Federico Firoozi, Jonathan Jedwab, Amarpreet Rattan

Let $a, b$ be fixed positive coprime integers. For a positive integer $g$ , write $W_{k} (g)$ for the set of lattice paths from the startpoint $(0, 0)$ to the endpoint $(g a, g b)$ with ste…

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.CO2023

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…

math.CO2022

A Comparison of Integer Partitions Based on Smallest Part

Damanvir Singh Binner, Amarpreet Rattan

For positive integers $n, L$ and $s$ , consider the following two sets that both contain partitions of $n$ with the difference between the largest and smallest parts bounded by $L$ :…

math.CO2021

$k$ -Factorizations of the full cycle and generalized Mahonian statistics on $k$ -forests

John Irving, Amarpreet Rattan

We develop direct bijections between the set $F_{n}^{k}$ of minimal factorizations of the long cycle $(01 \dots k n)$ into $(k + 1)$ -cycle factors and the set $R_{n}^{k}$ of rooted labe…

math.CO2020★ 2 cited

On Conjectures Concerning the Smallest Part and Missing Parts of Integer Partitions