The notation s(n, k) represents the Stirling numbers of the second kind, which count the number of ways to partition a set of n distinct objects into k non-empty subsets. These numbers are essential for understanding combinatorial structures, especially in partitioning sets and determining relationships between different arrangements. The Stirling numbers of the first kind are related but focus on permutations with cycles, making these two concepts complementary in enumerative combinatorics.
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