Philippa Holdridge

collaborators

4 papers

math.CO2026

On the Extended 1-2-3 Conjecture of Pilz

Philippa Holdridge, PÃ©ter PÃ¡l Pach

We resolve (for all sufficiently large $n$ ) a conjecture of Pilz on the symmetric difference $A I^ (2 A) I^ \dots I^ (n A)$ for finite sets $A \subseteq N$ of positive integers. W…

math.NT2026

Random Diophantine Equations in the Primes II

Philippa Holdridge

Let $d \geq 2$ and $n \geq d$ with $(d, n) \in / {(2, 2), (3, 3)}$ . We consider homogeneous Diophantine equations of degree $d$ in $n + 1$ variables and whether they have solutions in the…

math.NT2026

Random Diophantine Equations in the Primes

Philippa Holdridge

We consider equations of the form $a_{1} x_{1}^{k} + ... + a_{s} x_{s}^{k}$ and when they have solutions in the primes. We define an analogue of the Hasse principle for solubility in the…

math.NT2025

Additive Ramsey theory over Piatetski-Shapiro numbers

Jonathan Chapman, Sam Chow, Philippa Holdridge

We characterise partition regularity for linear equations over the Piatetski-Shapiro numbers $⌊ n^{c} ⌋$ when $1 < c < c^{a^} (s)$ , where $s ⩾ 3$ is the number of v…