Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Statistics of Lattice Polytopes   We use the notions of reflexivity and of reflexive dimensions in order to
introduce probability measures for lattice polytopes and initiate the
investigation of their statistical properties. Examples of applications to
discrete geometry include a study of randomness of self-duality of reflexive
polytopes and implications for expectation values of the numbers of such
polytopes in higher dimensions. We also discuss enumeration problems and
related algorithms and point out interesting open problems. In this context we
define the notion of IP-confined polytopes. Our new results include the list of
IP-simplices in 3 dimensions that are not IP-confined. The main motivation for
the study of these issues comes from applications in algebraic geometry and
string theory.

21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol