Exercises |

E:Prove Theorem directly.

E:Check the details of the second example .

E:AssumeXto be a finite set with subsetsX. Use the Principle of Inclusion and Exclusion in order to derive the number of elements of_{1}, ...,X_{n}Xwhich lie in preciselymof these subsetsX._{i}

E:Show thatf(n)= å_{d | n}d m(n/d), and n= å_{d | n}f(d).

E:Evaluate thederangement numberi.e. the number of fixed point free elementes inD_{n}:= | { pÎS_{ n}| " i În:pi not =i } | ,SDerive a recursion for these numbers and show that they tend to_{n}.1/e.

E:Prove the Two Involutions' Principle.

harald.fripertinger@kfunigraz.ac.at,

last changed: August 28, 2001

Exercises |