Let’s count – Partitions
Exercise 1.
Write how many ways there are to subdivide 4 people into 3 (nonempty) distinguishable groups (A, B, C) in two different ways:
a) by means of a known formula;
b) Count first partitions into 3 nonempty sets and then “label’’ the sets.
Exercise 2.
Recurrence formula for the Stirling numbers of II kind (solved in the pdf).
Let (nge 1, kge n+1). Prove that [Biglbracebegin{matrix}k newline nend{matrix}Bigrbrace=Biglbracebegin{matrix}k-1 newline n-1end{matrix}Bigrbrace+nBiglbracebegin{matrix}k – 1newline nend{matrix}Bigrbrace.] Deduce the values of the Stirling numbers of II type (Biglbracebegin{matrix}k newline nend{matrix}Bigrbrace) for (1le nle kle 4).
Combinatorics: Strategies and Methods for Counting
Combinatorics: Strategies and Methods for Counting
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