sniffnoy: (Dead face)
[personal profile] sniffnoy
So! I haven't posted here in a while. Several things I mean to post but I've been busy with other stuff. And most recently I've been busy with a return to the Snake problem!

So, at the suggestion of [personal profile] joshuazelinsky, I submitted the Snake problem as a second-year research problem to PROMYS. And the students (unfortunately I don't know their names, aside from one Rakesh Rivera) found that I made some incorrect claims! Here's a big one -- I said that Θ2,2,k was winnable, but in fact it's only winnable for k=1 and k=2!

So, yeah, I had to reevaluate some things. Was the family that Justin found actually winnable? Yes, it was. OK, but then how does one minimize it? (On here and on the webpage I only described the minimized version, but that's not how he described it to me; see the webpage, which now describes the non-minimized version.)

I haven't thoroughly checked it, but I think I have a corrected answer. My previous answer (again, see the webpage) was correct... when k≤m. For m>k, it's a bit more complicated. This is why Θ2,2,1 and Θ2,2,2 are winnable, but Θ2,2,k is not for k≥3. (In fact, Justin's graph is already minimal when m=2 and k≥3.)

But like I said, I think I've fixed it now!

Now to update more stuff. I'll be back with more posts later...

May 2025

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