1.5.6. Explain how to compute the inverse of a permutation that is given in two-line notation....
9. Let f be the following permutation in the symmetric group S9, written in two-line notation. 1 2 3 4 5 6 7 8 9 5 9 4 8 2 6 1 3 7 (a) Determine f3121 and explain why your answer is correct. (b) Determine ord(f) (c) Find a permutation p such that p-f
9. Let f be the following permutation in the symmetric group S9, written in two-line notation. 1 2 3 4 5 6 7 8 9...
Let wE S7 be a permutation which rearranges 7 objects as follows, showing the result on the lower line 2 3 4 6 7 5 5 4 2 7 6 1 3 a) Express was a product of disjoint cycles representing how each object moves Is w an even permutation, or an odd permutation? What is its order? products of disjoint cycles b) Calculate w3, w5 and w' 2 as c) Does there exist T E S7 for which T-lwr...
Problem 2: Let pı .. .pn E Sn be a permutation, considered in its one-line notation. A descent in p is an index 1 < i S n 1 such that p, > Pi+1. How many permutations in Sn have exactly one descent?
Can you explain to me how this works? Specifically, how does
the permutation multiplication work. How does (1,3,4,6)(2,3,5)
become the 2 permutations multiplied together. I guess I am lost on
all of it.
4. Let T = (1,3,4,6)(2,3,5) in Ss. Find the index of <T> in So. S61 Solution: If we let H = (r), then we are looking for (S. : H) However, we cannot simply claim that H = 12 because the cycle decomposition for T is not...
Problem 2: Let pı .. .pn E Sn be a permutation, considered in its one-line notation. A descent in p is an index 1 < i S n 1 such that p, > Pi+1. How many permutations in Sn have exactly one descent?
Problem 2: Let pı .. .pn E Sn be a permutation, considered in its one-line notation. A descent in p is an index 1 Pi+1. How many permutations in Sn have exactly one descent?
Python recursive function:
Given an ordered list L. A permutation of L is a rearrangement of its elements in some order. For example (1,3, 2) and (3, 2, 1) are two different permutations of L=(1,2,3). Implement the following function: def permutations (lst, low, high) The function is given a list 1st of integers, and two indices: low and high (lows high), which indicate the range of indices that need to be considered The function should return a list containing all...
The following questions pertain to permutations in S8 (a) Decompose the permutation (1 2 3 4 5 6 7 %) into a product of disjoint 13 6 4 1 8 2 5 7 cycles. = (b) Decompose the permutation T= (1,4, 3) (5,7,6,8) into a product of transpositions. (c) Determine whether o and T are even or odd permutations. (d) Compute the product OT.
ASAP
(3) (20 points) The following questions pertain to permutations in Sg. (a) Decompose the permutation o = (1 2 3 4 5 6 7 8) into a product of disjoint cycles. 3 6 4 1 8 2 5 (b) Decompose the permutation T = (1,4, 3) (5,7,6,8) into a product of transpositions. (c) Determine whether o and T are even or odd permutations. (d) Compute the productot.
Compute the Big O notation. Explain how you got the answer.
on W NA 1 public String modify (String str) { if (str.length() <= 1) return ""; int half = str.length() / 2; modify(str.substring(half)); 5} 1 2 3 for (int i = 0; i<n; i++) { for (int j 0; j < 5; j++) { for (int k = 0; k<n; k++) { 4 if ((i != j) && (i != k)) { 5 System.out.println(k); 6 } 7 } 8...
(3) (20 points) The following questions pertain to permutations in Sg. (a) Decompose the permutation o= (1 2 3 4 5 6 7 (3 6 4 1 8 25 ) into a product of disjoint cycles. (b) Decompose the permutation t = (1,4, 3) (5,7,6,8) into a product of transpositions. (c) Determine whether o and Tare even or odd permutations. (d) Compute the product ot.