For a set L of positive integers, a set system \({\mathcal F}\subseteq 2^{[n]}\) is said to be L-close Sperner, if for any pair F, G of distinct sets in \({\mathcal F}\) the skew distance \(sd(F,G)=\min \{|F\setminus G|,|G\setminus F|\}\) belongs to L. We reprove an extremal result of Boros, Gurvich, and Milanič on the maximum size of L-close Sperner set systems for \(L=\{1\}\), generalize it to \(|L|=1\), and obtain slightly weaker bounds for arbitrary L. We also consider the problem when L might include 0 and reprove a theorem of Frankl, Füredi, and Pach on the size of largest set systems with all skew distances belonging to \(L=\{0,1\}\).

对于一组大号正整数，一组系统\（{\ mathcal F} \ subseteq 2 ^ {[N]} \）被说成是大号-close Sperner，如果因为任何一对˚F，  ģ的不同组中\ （{\ mathcal F} \）的偏斜距离\（SD（F，G）= \分钟\ {| F \ setminus G |，| G \ setminus F | \} \）属于大号。我们证明了Boros，Gurvich和Milanič在\（L = \ {1 \} \）的L -close Sperner集系统的最大大小上的极值结果，将其推广为\（| L | = 1 \），并且获得任意L的较弱边界。我们还考虑了当L可能包含0并在所有偏斜距离都属于\（L = \ {0,1 \} \）的最大集合系统的大小上证明Frankl，Füredi和Pach定理。