On Füredi’s conjecture

We confirmed the following special case of Füredi’s conjecture:Let \(t\) $t$ be a non-negative integer. Let \( \mathcal{ P}=\{(A_i,B_i)\}_{1\leq i\leq m}\) $\mathcal{P}={\{(A_i,B_i)\}}_{1\le i\le m}$ be a set-pair family satisfying \(|A_i \cap B_i|\leq t\) $|A_i\cap B_i|\le t$ for \(1\leq i \leq m\) $1\le i\le m$ and \(|A_i\cap B_j|>t\) $|A_i\cap B_j|>t$ for all \(1\leq i\neq j \leq m\) $1\le i\ne j\le m$ . Define \(a_i:=|A_i|\) $a_i:=|A_i|$ and \(b_i:=|B_i|\) $b_i:=|B_i|$ for each \(i\) $i$ . Assume that there exists a positive integer \(N\) $N$ such that \(a_i+b_i=N\) $a_i+b_i=N$ for each \(i\) $i$ . Then \(\sum_{i=1}^m \frac{1}{{a_i+b_i-2t \choose a_i-t}}\leq 1.\) $$\sum _{i=1}^m\frac{1}{\left(\genfrac{}{}{0pt}{}{a_i+b_i-2t}{a_i-t}\right)}\le 1.$$