Robert J. Betts

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20102016

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Showing 2016 · math.NTShow all

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math.NT2016

Two Upper Bounds for both the van der Waerden Numbers $W (r, k + 1)$ and $W (r + 1, k)$ , that show the Existence of a Recurrence Relation

Robert J Betts

Using a method we have utilized previously, namely through a finite power series expansion which also sometimes is known as the "radix polynomial" representation of an integer, we…

math.NT2016

The Asymptotic Behaviors of $lo g_{r} W (r, k)$ and $lo g_{k} W (r, k)$ , when $W (r, k)$ is a van der Waerden Number

Robert J Betts

We derive the asymptotic behaviors of $lo g_{r} W (r, k)$ and $lo g_{k} W (r, k)$ , when $W (r, k)$ is a van der Waerden Number. We use the approach to consider the subsets on the real l…

Two Upper Bounds for both the van der Waerden Numbers W(r,k+1) and W(r+1,k), that show the Existence of a Recurrence Relation

The Asymptotic Behaviors of logr​W(r,k) and logk​W(r,k), when W(r,k) is a van der Waerden Number

Two Upper Bounds for both the van der Waerden Numbers $W (r, k + 1)$ and $W (r + 1, k)$ , that show the Existence of a Recurrence Relation

The Asymptotic Behaviors of $lo g_{r} W (r, k)$ and $lo g_{k} W (r, k)$ , when $W (r, k)$ is a van der Waerden Number