At #Integers2025 this spring, I collaborated with a new group and proved that Misere Partizan Arc Kayles is PSPACE-complete. That paper just went up on the arXiv: https://arxiv.org/abs/2511.21888

For that paper we implemented two new playable games: Misere Partizan Arc Kayles itself (https://kyleburke.info/DB/combGames/miserePartizanArcKayles.html) and a Normal-Play version of Bounded Constraint Logic (https://kyleburke.info/DB/combGames/normalBoundedConstraintLogic.html).

I'm especially excited about how clearly we talked about using Constraint Logic to provide computational hardness.

#CombinatorialGames #PSPACEComplete

Gamesters at conferences play games. #Red7 at lunch on the final day (day 4) of #Integers2025.

This was a great conference and a real blast to be a part of! Thanks to Bruce and all the organizers for letting me be a part of it.

On the way to #Integers2025 , I told my colleague, trapped in the car with me, that I was going to be lost in the #NumberTheory talks. I mused that all I remembered from abstract algebra that might be relevant was Cayley groups.

I didn't see that name (Cayley) until day three. I failed even at knowing what I wouldn't know.

The second day of #Integers2025 was excellent! I heard some great talks, especially one from Carrie Finch-Smith. Me and the other three gamesters I know about here also took some time and I think we found a game to be #PSPACE complete, so we're definitely going to be writing that up!

Tonight we got to see a tree that owns itself. Cool stuff!

The organizers have been totally awesome. Great conference so far!

#NumberTheory #CombinatorialGames

Day 1 of #Integers2025 just wrapped up! Integers is a #NumberTheory and #Combinatorics conference. There's historically a bit of CGT too. Here are my summaries of the #CombinatorialGames talks: https://combinatorialgametheory.blogspot.com/2025/05/integers-2025-cgt-talks.html

Two of the talks were the result of #UndergraduateResearch!