Apolarity for determinants and permanents of generic matrices
Commutative Algebra
2013-03-26 v2
Abstract
We show that the apolar ideals to the determinant and permanent of a generic matrix, the Pfaffian of a generic skew symmetric matrix and the Hafnian of a generic symmetric matrix are each generated in degree two. In each case we specify the generators and a Gr\"{o}bner basis of the apolar ideal. As a consequence, using a result of K. Ranestad and F. O. Schreyer we give lower bounds to the cactus rank and rank of each of these invariants. We compare these bounds with those obtained by J. Landsberg and Z. Teitler.
Keywords
Cite
@article{arxiv.1212.0515,
title = {Apolarity for determinants and permanents of generic matrices},
author = {Masoumeh Sepideh Shafiei},
journal= {arXiv preprint arXiv:1212.0515},
year = {2013}
}