OpenAI reports Foulkes’ conjecture for the sixth symmetric power
- Mathematics
For every integer b≥6 and finite-dimensional complex vector space V, there is a GL(V)-equivariant injection Sym⁶(Symᵇ V)→Symᵇ(Sym⁶ V).
OpenAI reports Foulkes’ conjecture for the sixth symmetric power
- Mathematics
For every integer b≥6 and finite-dimensional complex vector space V, there is a GL(V)-equivariant injection Sym⁶(Symᵇ V)→Symᵇ(Sym⁶ V).
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Read the background
For every integer b≥6 and finite-dimensional complex vector space V, there is a GL(V)-equivariant injection Sym⁶(Symᵇ V)→Symᵇ(Sym⁶ V).
Why it matters
If correct, proves the sixth-symmetric-power case for every permitted b and vector-space dimension.
What counts as progress
Does the sixth-power Foulkes injection hold for every b≥6?
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OpenAI reports Foulkes’ conjecture for the sixth symmetric power