Compute the sign of the following permutations: (a) (1, 4, 3, 6, 7)(5, 8, 9, 10). (b) σ ∈ Sn, i 7→ n + 1 − i. (c) Show that this initial configuration of the 15 puzzle is not solvable 3 1 15 13 2 8 5 9 12 7 11 4 14 6 10 − (d) Suppose that (i, j) ∈ Sn is a transposition and that i < j. Find an expression (in terms of i and j for the number of flips of (i, j).
Note: Please Update question I will update solution As b is not clear . And What is position of empty block in 15 puzzle?
Compute the sign of the following permutations: (a) (1, 4, 3, 6, 7)(5, 8, 9, 10). (b) σ ∈ Sn, i 7...
Q= II. Permutations. Consider the following permutations in Sg: 1 2 3 4 5 6 7 8 9 3 1 4 5 9 2 6 8 7 2 7 1 8 4 5 9 3 6 1. Express a and B as products of disjoint cycles. 2. Compute a-108-1 3. Find ord(a) and ord(B). 4. Express a and B as products of transpositions.
9, X = 3, 4, 5, and 7; compute Σ, (ΣΧ), and ΣΧ2 10. X EX --3, 0, 1, and 2; compute Σ(X-1), and D3-3 11. X-3,4,5, and 7; Y-1,0,1, and 2 compute ΣΧΥ and (DIP X-3, 4, 5, and 7; Ys-1,0,1, and 2; compute ΣΧ'ya and Σ(X-2)(Y-3) 's 4, 5, 6, and 9; Y -1,-1, 1, and 2; compute ΣΥ2 and Σ(X-5)(Y+ 1) 12. 13.
8 α = (д 1 9 2 5 3 4 5 10 3 6 7 86 9 10 2 7 10) 1 4 1 в = (1, 2 3 3 5 4 8 5 2 6 9 7 7 8 4 9 6 10 1 10) 10 8 ү 1 3 2 7 3 9 4 5 1 5 6 7 8 2 9 4 19) 10 1 ө ( 42 2 4 5 4 6 5 2 6 7...
This is all about abstract algebra of permutation group. 3. Consider the following permutations in S 6 5 3 489721)' 18 73 2 6 4 59 (a) Express σ and τ as a product of disjoint cycles. (b) Compute the order of σ and of τ (explaining your calculation). (c) Compute Tơ and στ. (d) Compute sign(a) and sign(T) (explaining your calculation) e) Consider the set Prove that S is a subgroup of the alternating group Ag (f) Prove that...
6. Compute the orders of the permutations (2 1 4 6 3), (1 2)(3 4 5) and (1 2)(34). 7. Compute the orders of the following products of non-disjoint cycles: (1 2 3)(2 3 4);(1 2 3)(3 2 4);(1 2 3)(3 4 5). Show your work Ans 6. The orders are 5, 6 and 2 respectively. 7. The orders are 2, 3 and 5.
a = 14. Consider the permutations (13)(24)(56) and B = (1 4)(26)(35) expressed in cycle notation. How many permutations y of {1,2,3,4,5,6} exist with the property B = y lay where we compose from left to right? (b) 48 (c) 6 (d) 24 (e) 3 (a) 8 1 15. You are given that {a,b,c} = {1,2,3} and, from the 8-puzzle 2 3 4 5 6 7 8 the following configuration has been reached by moving squares in and out of...
please answer all parts 10 9 8 7 6 5 4 3 2 1 9. I know which countries tend to cluster in similar sociocultural and economic groupi 10 9 8 7 6 5 4 3 2 1 2. I frequently attend seminars and lectures about other cultures or international topics. 10 9 8 7 6 5 4 3 2 1 3. I believe female expatriates can be equally as effective as male expatriates. 10. I feel capable of assessing...
Given the following sets: S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, Even numbers A = {2, 4, 6, 8, 10}; Odd number B = {3, 5, 7, 9}; Natural numbers N = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and Prime numbers C = {2, 3, 5, 7} Find the following: a) A ∪ C b) A ∩ N c) A ’ d) B ∩ N e) B ∪ N f) C...
(1) Write the permutation 1 2 3 4 5 6 7 8 9 10 7 5 10 3 8 9 6 2 4 ( 10 1 as a product of disjoint cycles.
X 3 5 7 5 6 7 9 4 8 6 Y 6 9 12 10 14 12 14 8 15 10 Discuss the relation between X and Y using an appropriate method. If possible, try to find the relation between X and Y treating X as independent variable?