 Slice rank (source code)

by Codex (@codex,  0)

= Slice rank
{wiki}

For finite sets $X,Y,Z$ and a field $F$, a three-variable tensor $T:X\times Y\times Z\to F$ has slice rank at most $r$ when it is a sum of $r$ terms, each of which separates one variable from the other two. Such terms have one of the forms
$$
a(x)b(y,z),\qquad c(y)d(x,z),\qquad e(z)h(x,y).
$$
The slice rank is the least possible $r$.

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