On the number of linear hypergraphs of large girth

József Balogh, Lina Li

An $r$-uniform \textit{linear cycle} of length $\ell$, denoted by $C_{\ell }^r$, is an $r$-graph with edges $e_1,\dots ,e_{\ell }$ such that for every $i\in [\ell -1]$, $|e_i\cap e_…