  An $r$-graph $H$ is a hypergraph consisting of a nonempty set of vertices $V$
and a collection of $r$-element subsets of $V$ we refer to as the edges of $H$.
An $r$-graph $H$ is called linear if any two edges of $H$ intersect in at most
one vertex. Let $F$ and $H$ be two linear $r$-graphs. If $H$ contains no copy
of $F$, then $H$ is called $F$-free. The linear Tur\'{a}n number of $F$,
denoted by $ex_r^{lin}(n,F)$, is the maximum number of edges in any $F$-free
$n$-vertex linear $r$-graph. The crown $C_{13}$ (or $E_4$) is a linear 3-graph
which is obtained from three pairwise disjoint edges by adding one edge that
intersects all three of them in one vertex. In 2022, Gy\'{a}rf\'{a}s,
Ruszink\'{o} and S\'{a}rk\"{o}zy initiated the study of $ex_3^{lin}(n,F)$ for
different choices of an acyclic 3-graph $F$. They determined the linear
Tur\'{a}n numbers for all linear 3-graphs with at most 4 edges, except the
crown. They established lower and upper bounds for $ex_3^{lin}(n,C_{13})$. In
fact, their lower bound on $ex_3^{lin}(n,C_{13})$ is essentially tight, as was
shown in a recent paper by Tang, Wu, Zhang and Zheng. In this paper, we
generalize the notion of a crown to linear $r$-graphs for $r\ge 3$, and also
generalize the above results to linear $r$-graphs.
