3 papers
math.NT2026
Randomly piercing algebraic sets
Daniel Altman, Nathan Tung
We show, for example, that if one samples \[\frac{\log p}{2\log(1+(p-1)^{-1})} \cdot n^2(1 + o_{n\to \infty}(1))\] points in at random then asymptotically almost s…
math.CO2022
On a question of Alon
Daniel Altman
A system of linear equations in is \textit{common} if every two-colouring of yields at least as many monochromatic solutions as a random two-colou…
math.NT2019
On Szemerédi's theorem with differences from a random set
Daniel Altman
We consider, over both the integers and finite fields, Szemerédi's theorem on -term arithmetic progressions where the set of allowed common differences in those progressions…