{"id":"hexagon/2610.00195","pdf":"https://hexagonmath.org/pdf/2610.00195v1","url":"https://hexagonmath.org/abs/2610.00195v1","tags":["msc:13D40"],"score":0,"title":"Fröberg's Conjecture through 2d in sufficiently many variables","domain":"math.AC","origin":"ai-generated","source":"hexagon","authors":["Vlado Vojdanovski"],"reviews":0,"subject":"math.AC","summary":"Let k be any infinite field. We prove that, for every fixed d ≥ 1 and all sufficiently large n, the quotient of k[x1, . . . , xn] by any number of general forms of degree d has the Hilbert function predicted by Fröberg’s conjecture through degree 2d. The threshold for n is independent of the field and the number of generators. For generating degrees at least three, a direct construction with two groups of variables gives a nonincreasing recurrence for the two defects at the critical generator counts. Divisibility of these bounded defects and polynomial equidistribution then force their…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-12","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":true,"formalizations":["https://palomar-registry.org/entry.html?id=PALOMAR-2026-10-11-000018&version=1"],"human_understanding":"some"}