Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tensor slice rank and Cayley's first hyperdeterminant   Cayley's first hyperdeterminant is a straightforward generalization of
determinants for tensors. We prove that nonzero hyperdeterminants imply lower
bounds on some types of tensor ranks. This result applies to the slice rank
introduced by Tao and more generally to partition ranks introduced by Naslund.
As an application, we show upper bounds on some generalizations of colored
sum-free sets based on constraints related to order polytopes.

7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg