Robert J. Betts

activity

20102016

collaborators

Showing cs.DMShow all

2 papers · 1 filter

cs.DM2016

A Radix Representation for each van der Waerden number $W (r, k)$ with $r$ colors: Why $lo g_{r} W (r, k) < k^{2}$ is true whenever $k$ is the number of terms in the arithmetic progression

Robert J Betts

Here we show that by expressing a van der Waerden number $W (r, k)$ by its radix polynomial representation, it not only is possible to locate each proper subset on $R$ in w…

cs.DM2016

How to find the least upper bound on the van der Waerden Number $W (r, k)$ that is some integer Power of the coloring Integer $r$

Robert J Betts

What is a least integer upper bound on van der Waerden number $W (r, k)$ among the powers of the integer $r$ ? We show how this can be found by expanding the integer $W (r, k)$ into p…

A Radix Representation for each van der Waerden number W(r,k) with r colors: Why logr​W(r,k)<k2 is true whenever k is the number of terms in the arithmetic progression

How to find the least upper bound on the van der Waerden Number W(r,k) that is some integer Power of the coloring Integer r

A Radix Representation for each van der Waerden number $W (r, k)$ with $r$ colors: Why $lo g_{r} W (r, k) < k^{2}$ is true whenever $k$ is the number of terms in the arithmetic progression

How to find the least upper bound on the van der Waerden Number $W (r, k)$ that is some integer Power of the coloring Integer $r$