Problem 4 Let o = (4573) and T = (46823) denote permutations in Sg (a.) Calculate the disjoint cycle decomposition for OT (b.) Find the order for OT (c.) Find all generators for (or) ≤ Sg. Express your answers in terms of (7)k for approrpriate k, no need to calculate the disjoint cycle decomposition for these generators.

Q: 4. Bijections and Permutations: a. Let t= 263198475 in one-line notation. Give two-line notation and…

A: (a) let τ=263198475  claim- give two line notation and cycle notation. then its inverse, square in…

Q: R.REF -1 1 0 1 -1 0 CT 5 -13 4 -9 -2 3 0 0 -1 -1 1002 0 1 0 0 0 1 0000 -1 -2

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Q: Let (a1a2a3a4) and (a5a6) be disjoint cycles in S10. Show that there isno element x in S10 such that…

A: Given: a1a2a3a4 and a5a6 are disjoint cycles in S10.We need to show that there is no element x in…

Q: (a) Let 7(n) be the number of divisors function and let (n) be the sum of divisors function.…

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Q: Model the following problem as a specified coefficient of an ordinary generating function. Follow…

A: Given information: Number of members in committees = 13 Number of officials in Country A = 5 Number…

Q: compute η2

A: η2  is given by : η2=SSbetweenSStotal

Q: Which of the following sets with an internal binary operation does not have an inverse for every…

A: The objective of the question is to identify which of the given sets does not have an inverse for…

Q: How do you derermine of RS → R* 76 onto?

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Q: Construct the multiplication table for Zs. Using this table, or otherwise, determine the following x…

A: Solution

Q: (a). Show that the addition of x²+x and x²+x+1 is in GF(2³) (b).Show that the multiplication of x²+x…

A: We know that GF(2m) are the binary polynomials, i.e. polynomial whose coefficients are either 0 or…

Q: . Find all of the conjugacy classes of elements of D14

A: Note: The notation of a dihedral group in different books varry from Dn to D2n. Here I consider it…

Q: Compute the powers Ak, k = 1, 2, 3, . . . , 2022.

A: A1 =A = 1100011000110001 Let's find A2 = A * A A2 = 1100011000110001 * 1100011000110001 A2 =…

Q: Observe the following pattern: 1 + 3 = 22 1 + 3 + 5 = 32 1 + 3 + 5 + 7 = 42  Find the next two lines…

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Q: In the characteristic polynomial (3 – A)(4 – A)³(–3- )(3 – 1), what is the multiplicity of d = -3?

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Q: A 3. What does Q.E.D stand for? I have proven what needs to be shown Quickly executed definition…

A: Given that we need to choose the correct statement from the given below  That  What does Q.E.D.…

Q: Matrix with rank A= 4 het A be a 5x6 ind cim Row A, dim Col A, dim Nul A, din Bow AT, dim Cal AT,…

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Q: (a) The Rodrigues formula says that H₂ (§) = (-1)"¹ es ² * (₁) * (1) Use it to derive H3 and H₁. (b)…

A: Since you have added many problem in one question, here I am answering first two parts (a) and (b).

Q: Topic: Sterling Number Relations. Give a formula for S(1000, 100) in terms of S(998, 98), S(998,…

A: Formula Used: S(n, k)= S(n-1, k-1) - (n-1) S(n-1, k)