find the number of partitions of a set Into k blocks

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clarko

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Hi guys could you help me with these questions please ?
r<=k<=n, S(n,k)^{r}
How I can find the number of partitions of a set {1...n} Into k blocks such that the elements {1...r} must be in different blocks ?
How I can find the recurrence relation ?
Thanks !!
 
What have you tried? Where are you stuck? This is a help forum where we help students solve their problems but we never solve problems for students.
If you had read the forum's posting guidelines and followed them, you would have received help by now.
 
No I don't need to have the solution,
Just a small induction will be helpful to start.
 
clarko said:
Hi guys could you help me with these questions please ?
r<=k<=n, S(n,k)^{r} How I can find the number of partitions of a set {1...n} Into k blocks such that the elements {1...r} must be in different blocks ? How I can find the recurrence relation ?
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Assuming that you do mean partitions of a set the fact is that the term BLOCKS is not used in western mathematics.
Definition: a partition of a nonempty set [imath]\mathcal{S}[/imath] is a collection of pairwise disjoint nonempty subsets of [imath]\mathcal{S}[/imath] call it [imath]\mathcal{P}[/imath], such that [imath]\bigcup\limits_{C \in P} C = \mathcal{S}[/imath] The sets [imath]C \in\mathcal{ P}[/imath] are known as cells not blocks.
Furthermore, you have posted an [imath]\bf n[/imath] while [imath]\bf r[/imath] another time.
Which is it? Or is it both? What are those numbers for?
It would seem that you need to correct and/or clarify the statement of your question.


[imath][/imath][imath][/imath]
 
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