Aaron Robertson

activity

19982026

most citedSome New Exact van der Waerden Numbers

26 citations · 52 across the 29 of their papers we have counts for

collaborators

30 papers

math.CO2026

On Hales-Jewett and Related Numbers

Nathan Conlon, Nayda Farnsworth, Aaron Robertson

We investigate the Hales-Jewett numbers and some variants of them, both computationally and via enumerative and probabilistic arguments. In particular, we give the improved lower b…

math.CO2025

Gallai-Schur Triples and Related Problems

Yaping Mao, Aaron Robertson, Jian Wang +2

Schur's Theorem states that, for any $r \in Z^{+}$ , there exists a minimum integer $S (r)$ such that every $r$ -coloring of ${1, 2, \dots, S (r)}$ admits a monochromatic solutio…

math.CO2024

A Multidimensional Rado Theorem

Aaron Robertson

We extend Deuber's theorem on $(m, p, c)$ -sets to hold over the multidimensional positive integer lattices. This leads to a multidimensional Rado theorem where we are guaranteed mono…

math.CO2018★ 1 cited

The Determination of 2-color zero-sum generalized Schur Numbers

Aaron Robertson, Bidisha Roy, Subha Sarkar

Consider the equation $E : x_{1} + \dots + x_{k - 1} = x_{k}$ and let $k$ and $r$ be positive integers such that $r ∣ k$ . The number $S_{z, 2} (k; r)$ is defined to be…

math.CO2018

Zero-sum Analogues of van der Waerden's Theorem on Arithmetic Progressions

Aaron Robertson

Let $r$ and $k$ be positive integers with $r ∣ k$ . Denote by $w_{z} (k; r)$ the minimum integer such that every coloring $χ:[1,w_{\mathrm{\mathfrak{z}}}(k;r)]…

math.CO2018★ 3 cited

Zero-sum Generalized Schur Numbers

Aaron Robertson

Let $r$ and $k$ be positive integers with $r ∣ k$ . Denote by $S_{z} (k; r)$ the minimum integer $n$ such that every coloring $χ:[1,n] \rightarrow \{0,1,\dots,r…