Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of symmetric maximal noncrossing collections of $k$-element
  sets   We investigate the existence of maximal collections of mutually noncrossing
$k$-element subsets of $\left\{ 1, \dots, n \right\}$ that are invariant under
adding $k\pmod n$ to all indices. Our main result is that such a collection
exists if and only if $k$ is congruent to $0, 1$ or $-1$ modulo
$n/\operatorname{GCD}(k,n)$. Moreover, we present some algebraic consequences
of our result related to self-injective Jacobian algebras.

36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph