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A tree is a connected graph without cycles, with a finite or infinite number of vertices. There are many variants of trees, according to further constraints or decorations.
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Shattering/covering finite trees, and a simple looking inequality
Consider the tree $T$ with the set of its maximal elements (denoted $[T]$) equal to $\prod_{m\leq n} X_m$ for some finite sets $X_0,..., X_n$. Let $p(T)=\{b: b\in \prod_{i\leq m \leq j } X_{m}\text{ f …