D. Conlon

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math.CO2025

Sums of algebraic dilates

David Conlon, Jeck Lim

We show that if $λ_{1}, \dots, λ_{k}$ are algebraic numbers, then $∣ A + λ_{1} \cdot A + \dots + λ_{k} \cdot A ∣ \geq H (λ_{1}, \dots, λ_{k}) ∣ A ∣ - o (∣ A ∣)$ for all finite subsets $A$ of $C$ , where $…

math.CO2025

Even cycles in graphs avoiding longer even cycles

David Conlon, Eion Mulrenin, Cosmin Pohoata

A conjecture of Verstraëte states that for any fixed $ℓ < k$ there exists a positive constant $c$ such that any $C_{2 k}$ -free graph $G$ contains a $C_{2 ℓ}$ -free subgraph with…

math.CO2024

Sums of dilates over groups of prime order

David Conlon, Jeck Lim

For $p$ prime, $A \subseteq Z / p Z$ and $λ \in Z$ , the sum of dilates $A + λ \cdot A$ is defined by \[A + λ\cdot A = \{a + λa' : a, a' \in A\}.\] The basic p…