A New Method to Construct Lower Bounds for Van der Waerden Numbers

@article{Herwig2007ANM,
  title={A New Method to Construct Lower Bounds for Van der Waerden Numbers},
  author={P. R. Herwig and Marijn Heule and P. M. van Lambalgen and Hans van Maaren},
  journal={Electr. J. Comb.},
  year={2007},
  volume={14}
}
We present the Cyclic Zipper Method, a procedure to construct lower bounds for Van der Waerden numbers. Using this method we improved seven lower bounds. For natural numbers r, k and n a Van der Waerden certificate W (r, k, n) is a partition of {1, . . . , n} into r subsets, such that none of them contains an arithmetic progression of length k (or larger). Van der Waerden showed that given r and k, a smallest n exists the Van der Waerden number W (r, k) for which no certificate W (r, k, n… CONTINUE READING

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