Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: No eleventh conditional Ingleton inequality   A rational probability distribution on four binary random variables $X, Y, Z,
U$ is constructed which satisfies the conditional independence relations $[X
\mathrel{\text{$\perp\mkern-10mu\perp$}} Y]$, $[X
\mathrel{\text{$\perp\mkern-10mu\perp$}} Z \mid U]$, $[Y
\mathrel{\text{$\perp\mkern-10mu\perp$}} U \mid Z]$ and $[Z
\mathrel{\text{$\perp\mkern-10mu\perp$}} U \mid XY]$ but whose entropy vector
violates the Ingleton inequality. This settles a recent question of Studen\'y
(IEEE Trans. Inf. Theory vol. 67, no. 11) and shows that there are, up to
symmetry, precisely ten inclusion-minimal sets of conditional independence
assumptions on four discrete random variables which make the Ingleton
inequality hold.

29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg