Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on traces of set families   A family of sets $\mathcal{F} \subseteq 2^{[n]}$ is defined to be $l$-trace
$k$-Sperner if for any $l$-subset $L$ of $[n]$ the family of traces
$\mathcal{F}|_L=\{F \cap L: F \in \mathcal{F}\}$ does not contain any chain of
length $k+1$. In this paper we prove that for any positive integers $l',k$ with
$l'<k$ if $\mathcal{F}$ is $(n-l')$-trace $k$-Sperner, then $|\mathcal{F}| \le
(k-l'+o(1))\binom{n}{\lfloor n/2\rfloor}$ and this bound is asymptotically
tight.

20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph