Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bruhat order on plane posets and applications   A plane poset is a finite set with two partial orders, satisfying a certain
incompatibility condition. The set PP of isoclasses of plane posets owns two
products, and an infinitesimal Hopf algebra structure is defined on the vector
space H_PP generated by PP, using the notion of biideals of plane posets. We
here define a partial order on PP, making it isomorphic to the set of
partitions with the weak Bruhat order. We prove that this order is compatible
with both products of PP; moreover, it encodes a non degenerate Hopf pairing on
the infinitesimal Hopf algebra H_PP.

34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg