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1: 26.14 Permutations: Order Notation
An excedance in σ 𝔖 n is a position j for which σ ( j ) > j . A weak excedance is a position j for which σ ( j ) j . The Eulerian number n k is equal to the number of permutations in 𝔖 n with exactly k excedances. It is also equal to the number of permutations in 𝔖 n with exactly k + 1 weak excedances. …