A lot has happened since my last post on the Zarankiewicz problem, so it's storytime, and will be for several posts to come. Let's be honest: storytime is better than mathstime, even in the opinion of many mathematicians.

  1. Keyboards and Projective Geometry
  2. The Zarankiewicz Rollercoaster
  3. How to beat Brute Force
  4. Zarankiewicz Algorithm 1: Backtracking Search
  5. Zarankiewicz Algorithm 1: Pruning the Search Tree

I do think I should spoil the ending, though, so you (dear reader) will know where it's going.

Long story short, as of 9pm last night I have $z(n,n)$ for every $n \le 31$, and this would have been an improvement on the previous record of $n \le 21$, except here's the punchline, from the arXiv this month:


Appendix: Small Zarankiewicz Numbers.


Well played, Narjess Afzaly and Professor Brendan McKay. Well played.


The good news is, my results are in complete agreement. Also, given the apparent interest in the problem, I thought it would be a good idea to start an online database for results on this and related problems, so I did.