5 papers
Strength and slice rank of forms are generically equal
Edoardo Ballico, Arthur Bik, Alessandro Oneto +1
We prove that strength and slice rank of homogeneous polynomials of degree over an algebraically closed field of characteristic zero coincide generically. To show this,…
Semi-algebraic properties of Minkowski sums of a twisted cubic segment
Arthur Bik, Adam Czapliński, Markus Wageringel
We find a semi-algebraic description of the Minkowski sum of copies of the bounded twisted cubic for each integer $n\ge…
The monic rank
Arthur Bik, Jan Draisma, Alessandro Oneto +1
We introduce the monic rank of a vector relative to an affine-hyperplane section of an irreducible Zariski-closed affine cone . We show that the monic rank is finite and greater…
Polynomials and tensors of bounded strength
Arthur Bik, Jan Draisma, Rob H. Eggermont
Notions of rank abound in the literature on tensor decomposition. We prove that strength, recently introduced for homogeneous polynomials by Ananyan-Hochster in their proof of Stil…
Noetherianity up to conjugation of locally diagonal inverse limits
Arthur Bik
We prove that the inverse limit of the sequence dual to a sequence of Lie algebras is Noetherian up to the action of the direct limit of the corresponding sequence of classical alg…