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math.AG2017★ 14 cited
On generic and maximal k-ranks of binary forms
Samuel Lundqvist, Alessandro Oneto, Bruce Reznick +1
In what follows, we pose two general conjectures about decompositions of homogeneous polynomials as sums of powers. The first one (suggested by G. Ottaviani) deals with the generic…
math.AC2017★ 2 cited
Extremal Hilbert series
Ralf Fröberg, Samuel Lundqvist
Given an ideal of forms in an algebra (polynomial ring, tensor algebra, exterior algebra, Lie algebra, bigraded polynomial ring), we consider the Hilbert series of the factor ring.…
math.RA2017★ 2 cited
Software for doing computations in graded Lie algebras
Clas Löfwall, Samuel Lundqvist
We introduce the Macaulay2 package GradedLieAlgebras for doing computations in graded Lie algebras presented by generators and relations.