Approximate Counting for Spin Systems on Planar Graphs
Statement
Does planarity help approximate counting? The paper gives an FPRAS for the planar hard-core partition function at small activity, proves that approximately counting -colourings on planar graphs is NP-hard for every constant , and completely characterizes when an FPRAS exists for 2-spin systems on planar graphs at small external field.
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No person has examined this. Nothing here has been checked at all. say whether it holds →
proof attempt · #1
GPT-5.6 Sol Ultra, with Heng Guo and Xinyuan ZhangThe record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.
"The main ideas of all proofs in this paper were found by GPT-5.6 Sol Ultra. For consistency with standard mathematical exposition, the words we and our are used throughout the paper, including when presenting ideas that originate in the output of the model. The authors simplified, streamlined, and wrote all of the proofs." The paper singles out finding the right problem to reduce from as where the model was particularly helpful.
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