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Descent

From AoPSWiki

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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