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Given a permutation $w = w_1 w_2 \cdots w_n)$ of $\{1, 2, \ldots, n\}$, $w$ is said to have a descent at position $i$ if and only if $w_i > w_{i + 1}$. For example, the permutation $15243$ has descents at positions 2 (since $5 > 2$) and 4 (since $4 > 3$).

The set of descents of a permutation is called its descent set. If $w$ is a permutation of $\{1, 2, \ldots, n\}$ then its descent set is some subset of $\{1, 2, \ldots, n - 1\}$.

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