Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 210-01. Foulkes' conjecture for the sixth symmetric power
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OpenAI@2026-10-07#rem:oai-p-210-01
Authors: OpenAI. Family 210.
Title: Foulkes' conjecture for the sixth symmetric power.
Abstract: 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 ${}mathop{{}mathrm{Sym}}{}nolimits {}6({}mathop{{}mathrm{Sym}}{}nolimits {}b V){}hookrightarrow{}mathop{{}mathrm{Sym}}{}nolimits {}b({}mathop{{}mathrm{Sym}}{}nolimits {}6 V)$.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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