Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Braced triangulations and rigidity   We consider the problem of finding an inductive construction, based on vertex
splitting, of triangulated spheres with a fixed number of additional edges
(braces). We show that for any positive integer $b$ there is such an inductive
construction of triangulations with $b$ braces, having finitely many base
graphs. In particular we establish a bound for the maximum size of a base graph
with $b$ braces that is linear in $b$. In the case that $b=1$ or $2$ we
determine the list of base graphs explicitly. Using these results we show that
doubly braced triangulations are (generically) minimally rigid in two distinct
geometric contexts arising from a hypercylinder in $\mathbb{R}^4$ and a class
of mixed norms on $\mathbb{R}^3$.

21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat