APOLARITY FOR DETERMINANTS AND PERMANENTS OF GENERIC MATRICES

被引：13
作者：
Shafiei, Sepideh Masoumeh [1 ]
机构：
[1] Northeastern Univ, Dept Math, Boston, MA 02115 USA
来源：
JOURNAL OF COMMUTATIVE ALGEBRA | 2015年 / 7卷 / 01期
关键词：
Determinant; permanent; Pfaffian; hafnian; apolar ideal; Waring rank; cactus rank; Grobner basis; GROBNER BASES; RANK;
D O I：
10.1216/JCA-2015-7-1-89
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 2. As a consequence, using a result of Ranestad and Schreyer, we give lower bounds to the cactus rank and rank of each of these invariants. We compare these bounds with those obtained by Landsberg and Teitler.
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页码：89 / 123
页数：35
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