Unformatted text preview: C&O 330 - ASSIGNMENT #4 DUE FRIDAY, 19 NOVEMBER AT 10:31PM (1) (20 points) (a) (15 points) Let u ↔ < and d ↔≥ . Let a 1 , . . . , a 4 be positive integers. Find the number of permutations with pattern u a 1- 1 du a 2- 1 du a 3- 1 du a 4- 1 , expressing your result as a determinant of binomial numbers. (b) (5 points) On the basis of this evidence state a conjecture of the number of permutations with pattern u a 1- 1 du a 2- 1 d ··· u a m- 1 du a m +1- 1 . (2) (20 points) A dodecahedron is a regular solid consisting of 12 regular pentagons arranged so that each vertex of the dodecahedron is incident with 3 pentagons and that every edge of the dodecahedron is incident with 2 pentagons. (a) (15 points) Find the cycle index polynomial for the automorphism group of the dodecahedron acting on the 12 faces of the dodecahedron. (b) (5 points) Find the generating series for the number of ways of paint- ing the faces of the dodecahedron with two colours....
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- Spring '05
- Elementary algebra, Dodecahedron