Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Chromatic numbers of stable Kneser hypergraphs via topological
  Tverberg-type theorems   Kneser's 1955 conjecture -- proven by Lov\'asz in 1978 -- asserts that in any
partition of the $k$-subsets of $\{1, 2, \dots, n\}$ into $n-2k-3$ parts, one
part contains two disjoint sets. Schrijver showed that one can restrict to
significantly fewer $k$-sets and still observe the same intersection pattern.
Alon, Frankl, and Lov\'asz proved a different generalization of Kneser's
conjecture for $r$ pairwise disjoint sets. Dolnikov generalized Lov\'asz'
result to arbitrary set systems, while K\v{r}\'{i}\v{z} did the same for the
$r$-fold extension of Kneser's conjecture. Here we prove a common
generalization of all of these results. Moreover, we prove additional
strengthenings by determining the chromatic number of certain sparse stable
Kneser hypergraphs, and further develop a general approach to establishing
lower bounds for chromatic numbers of hypergraphs using a combination of
methods from equivariant topology and intersection results for convex hulls of
points in Euclidean space.

26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc