MATH 475 Final: MATH475 BOYLE-M SPRING2005 0101 FINAL EXAM

• School: University of Maryland
• Department: Mathematics
• Course: MATH 475
• Professor: All

Document Summary

Math 475 spring 2005 final exam (take-home part) You may use books (although they"re not necessary), but you may not consult with other people. When the answer is a number, compute the number, not only a formula in numbers e. g. , from 5! Each problem is worth 15 points: let be a random permutation of the set {1, 2, . Explain: let g be the directed graph with adjacency matrix a = 3 5. 4 2!. (here a(i, j) is the number of edges in g from vertex i to vertex j. ) Let pn denote the number of paths of length n from vertex 1 to vertex 2 (these are the paths of n edges beginning at vertex. Compute limn 7 npn : a permutation is an involution if every cycle has length 1 or length 2. (in other words, composing the permutation with itself gives the identity permutation. ) Let an denote the number of permutations of {1, 2, .