{"id":"openai-math/Foulkes-Conjecture-for-the-Sixth-Symmetric-Power","pdf":"https://github.com/openai/math/blob/main/preprints/Foulkes-Conjecture-for-the-Sixth-Symmetric-Power-September-25-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/Foulkes-Conjecture-for-the-Sixth-Symmetric-Power-September-25-2026","tags":["representation-theory","invariant-theory","symmetric-powers"],"score":0,"title":"Foulkes' conjecture for the sixth symmetric power","domain":"Algebra","family":"210","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.RA","summary":"We prove the sixth-symmetric-power case of Foulkes' conjecture. For every integer b ≥ 6 and every finite-dimensional complex vector space V , there is a $`\\mathop{\\mathrm{GL}}\\nolimits (V)`$-equivariant injection $`\\mathop{\\mathrm{Sym}}\\nolimits ^6(\\mathop{\\mathrm{Sym}}\\nolimits ^b V)\\hookrightarrow\\mathop{\\mathrm{Sym}}\\nolimits ^b(\\mathop{\\mathrm{Sym}}\\nolimits ^6 V)`$.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":false,"family_title":"Foulkes' conjecture for sixth powers and quadratic stabilization"}