TY - JOUR
T1 - A Bound for the Waring Rank of the Determinant via Syzygies
AU - Boij, Mats
AU - Teitler, Zach
N1 - Publisher Copyright:
© 2019 Elsevier Inc.
PY - 2020/2/15
Y1 - 2020/2/15
N2 - We show that the Waring rank of the 3×3 determinant, previously known to be between 14 and 18, is at least 15. We use syzygies of the apolar ideal, which have not been used in this way before. Additionally, we show that the symmetric cactus rank of the 3×3 permanent is at least 14.
AB - We show that the Waring rank of the 3×3 determinant, previously known to be between 14 and 18, is at least 15. We use syzygies of the apolar ideal, which have not been used in this way before. Additionally, we show that the symmetric cactus rank of the 3×3 permanent is at least 14.
KW - Determinants
KW - Permanents
KW - Symmetric cactus rank
KW - Symmetric rank
KW - Syzygies
KW - Waring rank
UR - http://www.scopus.com/inward/record.url?scp=85074761605&partnerID=8YFLogxK
UR - https://scholarworks.boisestate.edu/math_facpubs/233
U2 - 10.1016/j.laa.2019.11.007
DO - 10.1016/j.laa.2019.11.007
M3 - Article
SN - 0024-3795
VL - 587
SP - 195
EP - 214
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
ER -