{"id":"openai-math/A-power-improvement-in-the-Heilbronn-triangle-lower-bound","pdf":"https://github.com/openai/math/blob/main/preprints/A-power-improvement-in-the-Heilbronn-triangle-lower-bound-September-25-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-power-improvement-in-the-Heilbronn-triangle-lower-bound-September-25-2026","tags":["discrete-geometry","heilbronn-problem","combinatorics"],"score":0,"title":"A power improvement in the Heilbronn triangle lower bound","domain":"Combinatorics","family":"191","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CO","summary":"There are absolute constants $`\\eta,c_1\\gt 0`$ such that, for every sufficiently large integer n , one can choose n points in the unit square so that every triangle they determine has area at least $`c_1n^{-2+\\eta}`$. Thus the almost n −2 upper-bound formulation of Heilbronn's triangle problem is false. The exponent η is fixed but extremely small.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":false,"family_title":"A power improvement in the Heilbronn triangle lower bound"}