徐子翔

In 1966, Kleitman established that if \( |A \triangle B| \leq d \) for any \( A, B \in \mathcal{F} \), then \( |\mathcal{F}| \leq \sum_{i=0}^{k} \binom{n}{i} \) for \( d = 2k \), and \( |\mathcal{F}| \leq 2 \sum_{i=0}^{k} \binom{n-1}{i} \) for \( d = 2k+1 \). These upper bounds are attained by the …