Improved Lower Bounds for Van Der Waerden Numbers
Improved Lower Bounds for Van Der Waerden Numbers
Recently, Ben Green proved that the two-color van der Waerden number ω(3, k) is bounded from below by $${k^{{b_0}\left( k \right)}}$$ where $${b_0}\left( k \right) = {c_0}{\left( {{{\log \,k} \over {\log \log \,k}}} \right)^{1/3}}$$ . We prove a new lower bound of kb(k) with $$b\left( k \right) = {{c\log \,k} …