TU Wien:Diskrete Mathematik für Informatik VO (Drmota)/Prüfung 2013-03-01

1 a) GF of a_i is A(x), GF of b_i is B(x), what is the GF of: $c_{n}=\sum _{k=0}^{n}{a_{n}b_{n-k}}$

1 b) Find the GF of: $d_{n}=1+\sum _{k=0}^{n}{d_{k}(n-k)}$

2) Möbius of:

    1
  /   \
 a    b
 |    |
 |    c
  \  /
   0

3) Dijkstra of a given graph (of ~ 8 nodes)

4) a) ir/reducible polynomials, both of degree 3 in Z3

b) $x^{3}\equiv 1mod3$

$12x\equiv 15mod21$