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math.CO2021★ 1 cited
Saturation of Rota's basis conjecture
Damir Yeliussizov
We prove an asymptotic saturation-type version of Rota's basis conjecture. It relies on the connection of Tao's slice rank with unstable tensors from geometric invariant theory.
math.CO2021
Tensor slice rank and Cayley's first hyperdeterminant
Alimzhan Amanov, Damir Yeliussizov
Cayley's first hyperdeterminant is a straightforward generalization of determinants for tensors. We prove that nonzero hyperdeterminants imply lower bounds on some types of tensor…