explain me clearly about Stirling number of second kind
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In mathematics, particularly in combinatorics, a Stirling number of the second kind (or Stirling partition number) is the number of ways to partition a set of n objects into k non-empty subsets and is denoted by {\displaystyle S(n,k)} S(n,k) or {\displaystyle \textstyle \lbrace {n \atop k}\rbrace } \textstyle \lbrace{n\atop k}\rbrace.[1] Stirling numbers of the second kind occur in the field of mathematics called combinatorics and the study of partitions.
Stirling numbers of the second kind are one of two kinds of Stirling numbers, the other kind being called Stirling numbers of the first kind (or Stirling cycle numbers). Mutually inverse (finite or infinite) triangular matrices can be formed from the Stirling numbers of each kind according to the parameters n, k.