Ben Green

collaborators

3 papers

math.CO2026

The proportion of permutations fixing a $k$ -set

Ben Green, Mehtaab Sawhney

Denote by $p (k)$ the limit, as $n \to \infty$ , of the probability that a random permutation on a set of size $n$ has an invariant set of size $k$ . We give an asymptotic for…

math.NT2026

Remarks on the inverse Littlewood conjecture

Thomas F. Bloom, Ben Green

The Littlewood conjecture, proven by Konyagin and McGehee-Pigno-Smith in the 1980s, states that if $A \subset Z$ is a finite set of integers with $∣ A ∣ = N$ then $\…

math.NT2024

Covering integers by $x^{2} + d y^{2}$

Ben Green, Kannan Soundararajan

What proportion of integers $n ⩽ N$ may be expressed as $x^{2} + d y^{2}$ for some $d ⩽ I^$ , with $x, y$ integers? Writing $I^$ as $(\log N)^{\log 2} 2^{Î±\sqrt{\log \lo…

The proportion of permutations fixing a k-set

Remarks on the inverse Littlewood conjecture

Covering integers by x2+dy2

The proportion of permutations fixing a $k$ -set

Covering integers by $x^{2} + d y^{2}$