{"id":"openai-math/Quadratic-Stabilization-of-the-Canonical-Foulkes-Howe-Map","pdf":"https://github.com/openai/math/blob/main/preprints/Quadratic-Stabilization-of-the-Canonical-Foulkes-Howe-Map-September-25-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Quadratic-Stabilization-of-the-Canonical-Foulkes-Howe-Map-September-25-2026","tags":["representation-theory","invariant-theory","symmetric-functions","algebra"],"score":0,"title":"Quadratic stabilization of the canonical Foulkes--Howe map","domain":"Algebra","family":"210","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.RA","summary":"For every finite-dimensional complex vector space V , we prove that the canonical Foulkes–Howe map $`\\mathop{\\mathrm{Sym}}\\nolimits ^b(\\mathop{\\mathrm{Sym}}\\nolimits ^a V)\\longrightarrow\\mathop{\\mathrm{Sym}}\\nolimits ^a(\\mathop{\\mathrm{Sym}}\\nolimits ^b V)`$ is surjective whenever a ≥ 2 and $`b\\ge a(a-1)`$. This gives a quadratic stabilization bound independent of $`\\dim V`$.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":true,"family_title":"Foulkes' conjecture for sixth powers and quadratic stabilization"}