Aaron Robertson

most citedSome New Exact van der Waerden Numbers

26 citations · 26 across the 3 of their papers we have counts for

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math.CO2005

On the degree of regularity of generalized van der Waerden triples

Nikos Frantzikinakis, Bruce Landman, Aaron Robertson

Let $1 \leq a \leq b$ be integers. A triple of the form $(x, a x + d, b x + 2 d)$ , where $x, d$ are positive integers is called an {\em (a,b)-triple}. The {\em degree of regularity} of the f…

math.CO2005★ 26 cited

Some New Exact van der Waerden Numbers

Bruce Landman, Aaron Robertson, Clay Culver

For positive integers $r, k_{0}, k_{1}, ..., k_{r - 1},$ the van der Waerden number $w (k_{0}, k_{1}, ..., k_{r - 1})$ is the least positive integer $n$ such that whenever ${1, 2, ..., n}$ is partition…

math.CO2005

On Monochromatic Ascending Waves

Tim LeSaulnier, Aaron Robertson

A sequence of positive integers $w_{1}, w_{2}, ..., w_{n}$ is called an ascending wave if $w_{i + 1} - w_{i} \geq w_{i} - w_{i - 1}$ for $2 \leq i \leq n - 1$ . For integers $k, r \geq 1$ , let $A W (k; r)$ be…