Exercise · ZW-STIRLING-NUMBER-OF-THE-SECOND-KIND-002 · ★☆☆ Basic
State the value of S(n,n) for any n≥1.
Choose one option.
Show answer
- B. 1
Explanation
With n blocks for n elements, each element sits alone in its own block, and there is only one way to do this. The value n! would require ordering the blocks, which is not counted here.
Review the concept: Stirling number of the second kind
The Stirling number of the second kind S(n,k) counts the partitions of a set of n elements into k nonempty, indistinguishable blocks.
\[S(n,k)=kS(n-1,k)+S(n-1,k-1)\]
More practice problems: stirling number of the second kind
- ZW-STIRLING-NUMBER-OF-THE-SECOND-KIND-001 How many partitions of a 3-element set into 2 nonempty blocks exist?
- ZW-STIRLING-NUMBER-OF-THE-SECOND-KIND-003 State what the Stirling number S(n,k) counts.
- ZW-STIRLING-NUMBER-OF-THE-SECOND-KIND-004 What is the value of S(n,1) for n≥ 1?
- ZW-STIRLING-NUMBER-OF-THE-SECOND-KIND-005 What is S(n,k) when k>n?
- ZW-STIRLING-NUMBER-OF-THE-SECOND-KIND-006 Use the recurrence to compute S(4,2).
- ZW-STIRLING-NUMBER-OF-THE-SECOND-KIND-007 Compute S(4,3) using S(n,k)=kS(n-1,k)+S(n-1,k-1) and S(3,3)=1.
- ZW-STIRLING-NUMBER-OF-THE-SECOND-KIND-008 Add the values S(3,k) for k=1,2,3 and state which Bell number this is.
- ZW-STIRLING-NUMBER-OF-THE-SECOND-KIND-009 How many ordered partitions of 3 elements into 2 nonempty blocks exist?
← ZW-STIRLING-NUMBER-OF-THE-SECOND-KIND-001 ZW-STIRLING-NUMBER-OF-THE-SECOND-KIND-003 →