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

  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.},
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


Publications referenced by this paper.
Showing 1-10 of 14 references

Some unknown Van der Waerden numbers

V. Chvátal
R.K. Guy et al., eds., Combinatorial Structures and their Applications, pages 31–33, (Gordon and Breach, New York, 1970) the electronic journal of combinatorics 12 • 2005
View 2 Excerpts

Satisfiability and Computing van der Waerden Numbers

M. R. Dransfield, L. Liu, V. W. Marek, M. Truszczynski
In The Electronic Journal of Combinatorics • 2004

Some Progression - free Partitions Constructed Using Folkman ’ s Method

R. Rabung John
Canadian Mathematical Bulletin • 2004

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