Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Using the Swing Lemma and Cz\'edli diagrams for congruences of planar
  semimodular lattices   A planar semimodular lattice $K$ is \emph{slim} if $\mathsf{M}_3$ is not a
sublattice of~$K$. In a recent paper, G. Cz\'edli found four new properties of
congruence lattices of slim, planar, semimodular lattices, including the
\emph{No Child Property}: \emph{Let~$P$ be the ordered set of join-irreducible
congruences of $K$. Let $x,y,z \in P$ and let $z$ be a~maximal element of $P$.
If $x \neq y$, $x, y \prec z$ in $P$, then there is no element $u$ of $P$ such
that $u \prec x, y$ in $P$.} We are applying my Swing Lemma, 2015, and a type
of standardized diagrams of Cz\'edli's, to verify Cz\'edli's four properties.

10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org