Gan–Han–Sun–Wang conjecture on large $Y_{k,b}$-tilings

Let $k>b>0$ and let $n,s,k,b$ be positive integers with

$$n\ge (2k-b)(s+1)-1.$$

Let $Y_{k,b}$ be the $k$-graph consisting of two edges intersecting in exactly $b$ vertices. If $H$ is a $k$-graph on $n$ vertices with no $Y_{k,b}$-tiling of size $s+1$, then

$$e(H)\le \max\left\{\binom{(2k-b)(s+1)-1}{k},\binom{n}{k}-\binom{n-s}{k}\right\}+o(n^k).$$

Gan–Han–Sun–Wang conjecture. The displayed asymptotic upper bound should hold. This conjecture generalizes the matching problem to tilings by two-edge hypergraphs with prescribed intersection. The case $s=0$ is stated in the supplied text to have been resolved by Frankl and Füredi; the general conjecture is reported as resolved by the paper, which proves the relevant asymptotic result.