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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

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What is the minimum number of covering subsets?

Fix a positive integer constant $C$. Let $S_1, S_2, \cdots , S_k$ be subsets of $\{ 1, 2, \cdots , N \}$. Let us call $S_1, S_2, \cdots , S_k$ a $C$-cover if for every subset $T$ of $\{ 1, 2, \cdots …
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