TY - JOUR
T1 - Some examples of forms of high rank
AU - Buczyński, Jarosław
AU - Teitler, Zach
N1 - Publisher Copyright:
© 2015, Universitat de Barcelona.
PY - 2016/9/1
Y1 - 2016/9/1
N2 - We describe some forms with greater Waring rank than previous examples. In 3 variables we give forms of odd degree with strictly greater rank than the ranks of monomials, the previously highest known rank. This narrows the possible range of values of the maximum Waring rank of forms in 3 variables. In 4 variables we give forms of odd degree with strictly greater than generic rank. In degrees ≥ 5 these are the first examples showing that there exist forms with Waring rank strictly greater than the generic value.
AB - We describe some forms with greater Waring rank than previous examples. In 3 variables we give forms of odd degree with strictly greater rank than the ranks of monomials, the previously highest known rank. This narrows the possible range of values of the maximum Waring rank of forms in 3 variables. In 4 variables we give forms of odd degree with strictly greater than generic rank. In degrees ≥ 5 these are the first examples showing that there exist forms with Waring rank strictly greater than the generic value.
KW - Apolarity
KW - Power sum decompositions
KW - Waring rank
UR - http://www.scopus.com/inward/record.url?scp=84983028167&partnerID=8YFLogxK
U2 - 10.1007/s13348-015-0152-0
DO - 10.1007/s13348-015-0152-0
M3 - Article
AN - SCOPUS:84983028167
SN - 0010-0757
VL - 67
SP - 431
EP - 441
JO - Collectanea Mathematica
JF - Collectanea Mathematica
IS - 3
ER -