8 citations · 13 across the 5 of their papers we have counts for
5 papers
The 3 x 3 x 3 hyperdeterminant as a polynomial in the fundamental invariants for SL(3,C) x SL(3,C) x SL(3,C)
Murray Bremner, Jiaxiong Hu, Luke Oeding
We briefly review previous work on the invariant theory of 3 x 3 x 3 arrays. We then recall how to generate arrays of arbitrary size m_1 x ... x m_k with hyperdeterminant 0. Our ma…
On Kruskal's theorem that every 3 x 3 x 3 array has rank at most 5
Murray R. Bremner, Jiaxiong Hu
In the first part of this paper, we consider 3 x 3 x 3 arrays with complex entries, and provide a complete self-contained proof of Kruskal's theorem that the maximum rank is 5. In…
Canonical forms of small tensors over F_2
Murray R. Bremner, Jiaxiong Hu
We consider multidimensional arrays with at most 27 entries over the field with two elements, and their equivalence classes for the action of the direct product of general linear g…
The fundamental invariants of 3 x 3 x 3 arrays
Murray R. Bremner, Jiaxiong Hu
We determine the three fundamental invariants in the entries of a array over as explicit polynomials in the 27 variables for $1 \le i,…
Lie invariants in two and three variables
Murray R. Bremner, Jiaxiong Hu
We use computer algebra to determine the Lie invariants of degree <= 12 in the free Lie algebra on two generators corresponding to the natural representation of the simple 3-dimens…