Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coincident-point rigidity in normed planes   A bar-joint framework $(G,p)$ is the combination of a graph $G$ and a map $p$
assigning positions, in some space, to the vertices of $G$. The framework is
rigid if every edge-length-preserving continuous motion of the vertices arises
from an isometry of the space. We will analyse rigidity when the space is a
(non-Euclidean) normed plane and two designated vertices are mapped to the same
position. This non-genericity assumption leads us to a count matroid first
introduced by Jackson, Kaszanitsky and the third author. We show that
independence in this matroid is equivalent to independence as a suitably
regular bar-joint framework in a normed plane with two coincident points; this
characterises when a regular normed plane coincident-point framework is rigid
and allows us to deduce a delete-contract characterisation. We then apply this
result to show that an important construction operation (generalised vertex
splitting) preserves the stronger property of global rigidity in normed planes
and use this to construct rich families of globally rigid graphs when the
normed plane is analytic.

30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ