31 research outputs found
Connections between conjectures of Alon-Tarsi, Hadamard-Howe, and integrals over the special unitary group
We show the Alon-Tarsi conjecture on Latin squares is equivalent to a very
special case of a conjecture made independently by Hadamard and Howe, and to
the non-vanishing of some interesting integrals over SU(n). Our investigations
were motivated by geometric complexity theory.Comment: 7 page
Stability of the Levi-Civita tensors and an Alon–Tarsi type theorem
We show that the Levi-Civita tensors are semistable in the sense of Geometric Invariant Theory, which is equivalent to an analogue of the Alon–Tarsi conjecture on Latin squares. The proof uses the connection of Tao’s slice rank with semistable tensors. We also show an application to an asymptotic saturation-type version of Rota’s basis conjecture