For skew Bollobás systems with |A_i| ≤ a and |B_i| ≤ b, the maximum |∪ A_i| is binom(a+b+1, a) - 1 and the maximum |∪ B_i| is binom(a+b+1, a+1) - 1.
Majumder, On the maximum number of points in a maximal intersecting family of finite sets,Combinatorica,37(2017), 87–97
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The maximum size of the partial ground set of skew Bollob\'{a}s systems
For skew Bollobás systems with |A_i| ≤ a and |B_i| ≤ b, the maximum |∪ A_i| is binom(a+b+1, a) - 1 and the maximum |∪ B_i| is binom(a+b+1, a+1) - 1.