This’ll be a short post. I screwed up with the partition stuff. I tried to share the project with a few mathematicians in the field who I thought might respond. Total silence. After a while, I decided to try and model it myself, see if I could find anything interesting. So I learned the basics of a mathematical programming tool called Sage.

Anyhow, it turns out that my alternative definition of the crank only almost works. The core issue is that, while the crank is determined correctly by my setup in most cases, it gets the sign wrong for the cranks of canonical partitions. The absolute value is perfect, but the whole thing is not quite there.

This is very dispiriting, but I still intend to look into it, see if these concepts still have any interesting properties that I haven’t noticed yet. Anyhow, that’s all.