# title
Permanent V. Determinant: An Exponential Lower Bound Assuming Symmetry

# abstract
Grenet's determinantal representation for the permanent is optimal among determinantal representations that are equivariant with respect to left multiplication by permutation and diagonal matrices (roughly half the symmetry group of the permanent). In particular, if any optimal determinantal representation of the permanent must be polynomially related to one with such symmetry, then Valiant's conjecture on permanent v. determinant is true.

# publicationOutlet
ITCS'16: PROCEEDINGS OF THE 2016 ACM CONFERENCE ON INNOVATIONS IN THEORETICAL COMPUTER SCIENCE

# nameOfConference
Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science

# publisher.label
Association for Computing Machinery (ACM)