Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Achieving rental harmony with a secretive roommate   Given the subjective preferences of n roommates in an n-bedroom apartment,
one can use Sperner's lemma to find a division of the rent such that each
roommate is content with a distinct room. At the given price distribution, no
roommate has a strictly stronger preference for a different room. We give a new
elementary proof that the subjective preferences of only n-1 of the roommates
actually suffice to achieve this envy-free rent division. Our proof, in
particular, yields an algorithm to find such a fair division of rent. The
techniques also give generalizations of Sperner's lemma including a new proof
of a conjecture of the third author.

31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys