{"id":"openai-math/Commuting-Division-Coefficient-Forms-and-the-Artinian-Eisenbud-Green-Harris-Conjecture","pdf":"https://github.com/openai/math/blob/main/preprints/Commuting-Division-Coefficient-Forms-and-the-Artinian-Eisenbud-Green-Harris-Conjecture-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Commuting-Division-Coefficient-Forms-and-the-Artinian-Eisenbud-Green-Harris-Conjecture-September-23-2026","tags":["commutative-algebra","hilbert-functions","algebraic-geometry"],"score":0,"title":"Commuting Division-Coefficient Forms and the Artinian Eisenbud--Green--Harris Conjecture","domain":"Algebra","family":"200","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.RA","summary":"We prove the Eisenbud–Green–Harris conjecture over every characteristic-zero field for homogeneous regular sequences of any positive length, with degrees at least two. Thus every homogeneous ideal containing such a sequence has the Hilbert function of a monomial ideal containing the corresponding pure powers.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"Eisenbud–Green–Harris and lex-plus-powers"}