Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Marriage Problem and the Fate of Bachelors   In the marriage problem, a variant of the bi-parted matching problem, each
member has a `wish-list' expressing his/her preference for all possible
partners; this list consists of random, positive real numbers drawn from a
certain distribution. One searches the lowest cost for the society, at the risk
of breaking up pairs in the course of time. Minimization of a global cost
function (Hamiltonian) is performed with statistical mechanics techniques at a
finite fictitious temperature.
  The problem is generalized to include bachelors, needed in particular when
the groups have different size, and polygamy. Exact solutions are found for the
optimal solution (T=0). The entropy is found to vanish quadratically in $T$.
Also other evidence is found that the replica symmetric solution is exact,
implying at most a polynomial degeneracy of the optimal solution.
  Whether bachelors occur or not, depends not only on their intrinsic
qualities, or lack thereof, but also on global aspects of the chance for pair
formation in society.

30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an