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On the minimum rank of a graph over finite fields
In this paper we deal with two aspects of the minimum rank of a simple undirected graph G on n vertices over a finite field Fq with q elements, which is denoted by mr(Fq,G). In the first part of this paper we show that ...
A proof of the set-theoretic version of the salmon conjecture
We show that the irreducible variety of 4 4 4 complex valued tensors of border rank at most 4 is the zero set of polynomial equations of degree 5 (the Strassen commutative conditions), of degree 6 (the Landsberg-Manivel ...