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.
- Keyboards and Projective Geometry
- The Zarankiewicz Rollercoaster
- How to beat Brute Force
- Zarankiewicz Algorithm 1: Backtracking Search
- 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:
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.