Aaron Robertson

activity

19982005

most citedSome New Exact van der Waerden Numbers

26 citations · 26 across the 5 of their papers we have counts for

collaborators

16 papers

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…

math.CO2003

Avoiding Monochromatic Sequences With Special Gaps

Bruce M. Landman, Aaron Robertson

For $S$ a set of positive integers, and $k$ and $r$ fixed positive integers, denote by $f (S, k; r)$ the least positive integer $n$ (if it exists) such that within every $r$ -coloring…

math.CO2002

Refined Restricted Involutions

Emeric Deutsch, Aaron Robertson, Dan Saracino

Define $I_{n}^{k} (α)$ to be the set of involutions of ${1, 2, ..., n}$ with exactly $k$ fixed points which avoid the pattern $α \in S_{i}$ , for some $i \geq 2$ , and define $I_n^k(\emptyset…

math.CO2002

Refined Restricted Permutations Avoiding Subsets of Patterns of Length Three

Toufik Mansour, Aaron Robertson

Define $S_{n}^{k} (T)$ to be the set of permutations of ${1, 2, ..., n}$ with exactly $k$ fixed points which avoid all patterns in $T \subseteq S_{m}$ . We enumerate $S_{n}^{k} (T)$ , $T \subsete…