Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $d$-cluster-free sets with a given matching number   Let $3\le d\le k$ and $\nu\ge 0$ be fixed and
$\mathcal{F}\subset\binom{[n]}{k}$. The matching number of $\mathcal{F}$,
denoted by $\nu(\mathcal{F})$, is the maximum number of pairwise disjoint sets
in $\mathcal{F}$, and $\mathcal{F}$ is $d$-cluster-free if it does not contain
$d$ sets with the union of size at most $2k$ and empty intersection. In this
paper, we give a lower bound and an upper bound for the maximum size of a
$d$-cluster-free family with a matching number at least $\nu+1$. In particular,
our result of the case $\nu=1$ settles a conjecture of Mammoliti and Britz. We
also introduce a Tur\'{a}n problem in hypergraphs that allows multiple edges,
which may be of independent interest.

10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ