Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The weak separation in higher dimensions   For an odd integer $r>0$ and an integer $n>r$, we introduce a notion of
weakly $r$-separated collections of subsets of $[n]=\{1,2,\ldots,n\}$. When
$r=1$, this corresponds to the concept of weak separation introduced by Leclerc
and Zelevinsky. In this paper, extending results due to Leclerc-Zelevinsky, we
develop a geometric approach to establish a number of nice combinatorial
properties of maximal weakly r-separated collections. As a supplement, we also
discuss an analogous concept when $r$ is even.

1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th