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The hard-square entropy constant
Find a closed form for the hard-square entropy constant κ ≈ 1.5030480825, the growth rate of independent sets in the square grid.
| 1 | { |
| 2 | "domain": "physics-astronomy", |
| 3 | "topics": [ |
| 4 | "statistical-mechanics", |
| 5 | "combinatorics" |
| 6 | ], |
| 7 | "type": "construction", |
| 8 | "source": { |
| 9 | "key": "horizonmath", |
| 10 | "name": "HorizonMath", |
| 11 | "url": "https://github.com/ewang26/HorizonMath/blob/4ef0b61a8a6d4c5ded661fab7c2e896af84abe6e/data/problems_full.json#L704-L714", |
| 12 | "id": "hard_square_entropy", |
| 13 | "curator": "Erik Y. Wang, Sumeet R. Motwani et al.", |
| 14 | "status": "open", |
| 15 | "as_of": "2026-10-20", |
| 16 | "catalog": "0521c19bbd38" |
| 17 | }, |
| 18 | "review": true, |
| 19 | "approval": "first-time" |
| 20 | } |