Andrew Lott

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20212026

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4 papers · 1 filter

math.CO2026

Refined upper bounds on Schur-like numbers

Swaroop Hegde, Andrew Lott, Giorgis Petridis +1

For positive integers $r, m$ and $N$ , every $r$ -coloring of ${1, \dots, N}$ contains a monochromatic solution to $x_{1} + \dots + x_{m + 1} = y_{1} + \dots + y_{m}$ provided that $N \ge 3^r (r!)^{…

math.CO2023

The sum-product problem for small sets

Ginny Ray Clevenger, Haley Havard, Patch Heard +3

For $A \subseteq R$ , let $A + A = {a + b : a, b \in A}$ and $AA = {ab : a, b \in A}$ . For $k \in N$ , let $S P (k)$ denote the minimum value of $max {∣ A + A ∣, ∣ AA ∣}$ over all $A…

math.CO2021

Schur's theorem in integer lattices

Vishal Balaji, Andrew Lott, Alex Rice

A standard proof of Schur's Theorem yields that any $r$ -coloring of ${1, 2, \dots, R_{r} - 1}$ yields a monochromatic solution to $x + y = z$ , where $R_{r}$ is the classical $r$ -color Ramsey…

math.CO2021

The pigenhole principle and multicolor Ramsey numbers

Vishal Balaji, Powers Lamb, Andrew Lott +4

For integers $k, r \geq 2$ , the diagonal Ramsey number $R_{r} (k)$ is the minimum $N \in N$ such that every $r$ -coloring of the edges of a complete graph on $N$ vertices yields o…