Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a Conjecture of Gowers on Clique Differences   We solve a conjecture of Gowers from 2009 on clique differences in chains,
thus ruling out any Sperner-type proof of the polynomial density Hales-Jewett
Theorem for alphabets of size $2$.

7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs