Permanent v. determinant: an exponential lower bound assumingsymmetry and a potential path towards Valiant's conjecture
Algebraic Geometry
2015-08-26 v2 Computational Complexity
Abstract
We initiate a study of determinantal representations with symmetry. We show that Grenet's determinantal representation for the permanent is optimal among determinantal representations respecting 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.
Keywords
Cite
@article{arxiv.1508.05788,
title = {Permanent v. determinant: an exponential lower bound assumingsymmetry and a potential path towards Valiant's conjecture},
author = {Joseph M. Landsberg and Nicolas Ressayre},
journal= {arXiv preprint arXiv:1508.05788},
year = {2015}
}