We give counter-examples that show W(k,l) > n in the webpages linked by "> n".
In those webpages, we display the set of numbers that belongs to each block.
One can verify that, with the setting, every number from [1 .. n] occurs
in exactly one block and no blocks have an arithmetic progression of length l.
Here is a perl script that can do the verfication. One needs to pass four arguments to the script: solution file, k, l, and n.
We are currently experimenting several van de Waerden number instances using bootstrapping technique. For each instance that we are testing now, we introduce two links to the pages that record the running status.
The "? n" link describes which value of n is being tested. For example, "? 412" located at W(4,4) shows that we are testing whether W(4,4) > 412. Inside the page, we display the statistics generated by bootstrapping program (with wsat(cc)).
The "stat" link for each W(k,l) instance being tested shows a brief summary of the running status. The first line is either "Done!" or "Running ...", depending on whether the test has finished or not. If it is still running, the "PID" gives the process ID that dynamically generates the summary. The next three lines give the number of restarts that have been done at this moment, the best result that we have got during the test, and the time when the summary is updated.
For convenience, the "stat" webpage will be refreshed every 30 seconds automatically.