Bruce M. Landman

activity

19992005

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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4 papers · 1 filter

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.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.CO1999

On Generalized Van der Waerden Triples

Bruce Landman, Aaron Robertson

Van der Waerden's classical theorem on arithmetic progressions states that for any positive integers k and r, there exists a least positive integer, w(k,r), such that any r-colorin…