Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Zone and double zone diagrams in abstract spaces   A zone diagram is a relatively new concept which was first defined and
studied by T. Asano, J. Matousek and T. Tokuyama. It can be interpreted as a
state of equilibrium between several mutually hostile kingdoms. Formally, it is
a fixed point of a certain mapping. These authors considered the Euclidean
plane and proved the existence and uniqueness of zone diagrams there. In the
present paper we generalize this concept in various ways. We consider general
sites in m-spaces (a simple generalization of metric spaces) and prove several
existence and (non)uniqueness results in this setting. In contrast to previous
works, our (rather simple) proofs are based on purely order theoretic
arguments. Many explicit examples are given, and some of them illustrate new
phenomena which occur in the general case. We also re-interpret zone diagrams
as a stable configuration in a certain combinatorial game, and provide an
algorithm for finding this configuration in a particular case.

27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga