Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quasiplanar diagrams and slim semimodular lattices   A (Hasse) diagram of a finite partially ordered set (poset) P will be called
quasiplanar if for any two incomparable elements u and v, either v is on the
left of all maximal chains containing u, or v is on the right of all these
chains. Every planar diagram is quasiplanar, and P has a quasiplanar diagram
iff its order dimension is at most 2. A finite lattice is slim if it is
join-generated by the union of two chains. We are interested in diagrams only
up to similarity. The main result gives a bijection between the set of the
(similarity classes of) finite quasiplanar diagrams and that of the (similarity
classes of) planar diagrams of finite, slim, semimodular lattices. This
bijection allows one to describe finite posets of order dimension at most 2 by
finite, slim, semimodular lattices, and conversely. As a corollary, we obtain
that there are exactly (n-2)! quasiplanar diagrams of size n.

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The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys