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For questions on linear extensions of posets.
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Entropy of chain decompositions of posets
Let $P$ be a finite poset and let $\,\mathcal{C}=(C_1,\ldots,C_\ell)\,$ be its decomposition into chains. We can define
$$
f(\mathcal{C}) = |C_1|! \, \cdots \,|C_\ell|!
$$
and ask for what $\mathcal{ …