Explain why every permutation in S(n) can be represented by a product of n-1 or fewer...

Explain why every permutation in S(n) can be represented by a product of n-1 or fewer cycles of length 2 (transpositions). Represent the permutationσ in problem (1) above as a product of 8 or fewer transpositions. Is σ an even or an odd permuation?

Expert Solution

Colby Messinger answered 2 years ago

what is the maximum number of inversions that a permutation {1,..,n} can have? give the unique...

what is the maximum number of inversions that a permutation {1,..,n} can have? give the unique permutation with this many inversions. how many permutations have one fewer inversions than the minimum.

Write down every permutation in S3 as a product of 2-cycles in the most efficient way...

Write down every permutation in S3 as a product of 2-cycles in the most efficient way you can find (i.e., use the fewest possible transpositions). Now, write every permutation in S3 as a product of adjacent 2-cycles, but don’t worry about whether your decomposition are efficient. Any observations about the number of transpositions you used in each case? Think about even versus odd.

1. prove s(n, k) = s(n − 1, k − 1) − (n − 1)s(n −...

1. prove s(n, k) = s(n − 1, k − 1) − (n − 1)s(n − 1, k). 2. What is ∑n k=0 s(n, k)?

Project #1. Goldbach Conjecture. “Every even integer greater than 2 can be represented as the sum of...

Project #1. Goldbach Conjecture. “Every even integer greater than 2 can be represented as the sum of two prime numbers.” For this project show the sums from 100,000 to 100,200. (1) Print it as follows: 100,000 prime no. 1prime no. 2 100,002…… 100,004…… ……… ……… 100,200…… (Of course, if you find that there is no such pair of primes, indicate the first number that does have a Goldbach pair. I don’t think you’ll find such a number!) (2) Also, print out...

Find a subgroup G in symmetric (permutation) group Sn such that (1) n = 4 and...

Find a subgroup G in symmetric (permutation) group Sn such that (1) n = 4 and G is abelian noncyclic group (2) n = 8 and G is dihedral group.

In this program, the user will enter some permutation of the integers 0 to n-1, inclusive,...

In this program, the user will enter some permutation of the integers 0 to n-1, inclusive, (each integer in that range will appear exactly once) followed by -1 to indicate the end of the input. The user will never input more than 100 numbers. Your job is to store all the numbers in an array in the order they are input. For example if the user inputs 3 0 2 1 -1 then you should store the 3 at index...

1. In 100 words or fewer, explain how managers can use budgets for planning. 2. In...

1. In 100 words or fewer, explain how managers can use budgets for planning. 2. In 100 words or fewer, explain the differences between participative budgeting and traditional budgeting. 3. In 100 words or fewer, explain when a management would prefer a flexible budget as opposed to a static budget

Algae can be represented as C106H263O110N16P. Calculate the mass ratio of N/P in algae. If the...

Algae can be represented as C106H263O110N16P. Calculate the mass ratio of N/P in algae. If the concentration of the total nitrogen in a lake is 12mg/L and the concentration of total phosphorus is 2mg/L, calculate the mass ratio of N/P in the lake. Is this body of water limited by phosphorus or nitrogen?

1. Create a scenario that can be used to model a counting question (permutation, combination or...

1. Create a scenario that can be used to model a counting question (permutation, combination or neither.) 2. Create a scenario that can be used to model a counting question (permutation, combination or neither.) 3. Create a scenario that can be used to model a counting question with multiple 'not', 'and', 'or' clauses

Explain why a generic drug product can be a pharmaceutical equivalent but not identical to the...

Explain why a generic drug product can be a pharmaceutical equivalent but not identical to the brand drug product?

Question