{"id":"openai-math/Polynomial-removal-fails-for-ordered-binary-matrices","pdf":"https://github.com/openai/math/blob/main/preprints/Polynomial-removal-fails-for-ordered-binary-matrices-September-25-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Polynomial-removal-fails-for-ordered-binary-matrices-September-25-2026","tags":["extremal-combinatorics","binary-matrices","combinatorics"],"score":0,"title":"Polynomial removal fails for ordered binary matrices","domain":"Combinatorics","family":"190","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CO","summary":"We construct a fixed $`66\\times66`$ binary matrix for which ordered matrix removal has no polynomial bound. This disproves the polynomial ordered binary matrix-removal conjecture. Ordered copies preserve the separate row and column orders and match both zeros and ones; removal permits changing entries in either direction.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":true,"family_title":"Polynomial removal fails for ordered binary matrices"}