Answer by Ulli for Antichains and chains in partial orders
Here is an example:For $i = 1, \ldots, 10$ define$a_i = \{i\}, \space b_i =\{1, \ldots, 10\} \cup \{i+10\}$Moreover, $c = \{1, \ldots, 20\}$.$A = \{a_i: 1 \le i \le 10\}$,$B = \{b_i: 1 \le i \le 10\}$,...
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Task: Give an example of a partial order in which there are exactly two antichains of size 10, and these antichains do not intersect; and there are exactly 100 chains of size 3 (the size of the chain...
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