Approximate Counting for Spin Systems on Planar Graphs
Does planarity help approximate counting? The paper gives an FPRAS for the planar hard-core partition function at small activity, proves that approximately counting $q$-colourings on planar graphs is NP-hard for every constant $q \geq 4$, and completely characterizes when an FPRAS exists for 2-spin systems on planar graphs at small external field.
Exact FrontierDelta
Scope and record
Occurred: Aug 6, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-discovered. Imported under CC BY 4.0.
Canonical aliases: Approximate Counting for Spin Systems on Planar Graphs · Planar spin systems
Confidence: Not scored
Registry verification: unreviewed · preprint · resolved
Attribution
VibeMathed
registry · event recorded by
Heng Guo
human · human collaborator
Xinyuan Zhang
human · human collaborator
GPT-5.6 Sol Ultra
model · ai model contributor · OpenAI
Lineage and corrections
This event attributed to Xinyuan Zhang
This event attributed to Heng Guo
This event attributed to GPT-5.6 Sol Ultra