Find the number of inversions in the permutation 52134 of Sz = {1,2, 3, 4, 5}. 6 O 5

Q: A student claims that he does not need to define permuta- tions because he knows the Fundamental…

A: A permutation is the arrangement of objects where the order of arrangement is considered. The…

Q: Let A = {1,2,3,4,5,6} and p1 = (4,2,5) and p2 = (2,6,1) be permutations of A. Compute p,-1 o p2¬1…

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Q: 14. Let A = {1,2,3,4,5,6} and p₁ = (4,2,5) and p₂ = (2,6,1) be permutations of A. Compute p₂¹P₁-1…

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Q: The distinct characteristic roots corresponding to the recurrence relation an=7an-1 -10an-2 are:…

A: The given recurrence relation is an=7an-1-10an-2. Rewrite the recurrence relation is an=7an-1-10an-2…

Q: Theorem. If n is composite, then there exists at least one pair of zero divisors in Zn.

A: This is quite a simple question and can be solved using basic definition of zero divisor and prime…

Q: 13. Is (Sn,) a commutative(abelain)? Is (Sn,) cyclic?

A: Solution is given as below :

Q: 1. Find all cquivalent classes determined by congruence modulo 5 on Z.

A: The equivalent classes under modulo n is defined by, a=x∈ℤ: x≡amod nIn the question n=5a=x∈ℤ: x≡amod…

Q: Let r(n) be the number of n-permutations whose square is the identity permutation. Prove that if n >…

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Q: The generators of Z12 are: O {1,3,7,11} O {1,5,7,11} O {1,3,5,7,11} O {1,5,7,8,11} O O O O

A: Generators of Zn are 'a' such that: gcd (a ,n)= 1.

Q: The distinct characteristic roots corresponding to the recurrence relation an=7an-1 -10an-2 are:…

A: Substitute the value of , we get

Q: Prove that ?? is generated by the following n-1 transpositions: (1 2), (2 3), (3 4),. . . , (n-1 n)

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Q: Use Euclid's Algorithm to show that there are integers s and t such that 21s + 97t 1. Showing all…

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Q: (2). What is the binary representation of the following: (a) (64.37109375) 10.

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Q: Let o be a fixed odd permutation in Sn. Show that every odd permutation in S, can be written as a…

A: The main objective is to prove that every odd permutation can be expressed as σα for some α even…

Q: 12. Suppose that k is a divisor of n. Prove that Z,/(k)~ Zp.

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Q: (5) Show that if n ɛ Z+ is odd which is divisible by k distinct primes, then the congruence x2 = 1…

A: Chinese Remainder Theorem: If a1,a2,...,ak are integers, and m1,m2,...,mk are pairwise relatively…

Q: Show that a permutation with odd order must be an even permutation

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Q: Consider the pseudorandom number generator given in our lessons: with Uf +1 = (auf + b) mod m…

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Q: Exercise 14.6.11. Suppose a is an an even or odd permutation? n-cycle. How can you tell whether a is

A: EX 14.6.11 : If σ=(a1 a2 a3....an), We need to explain how can we identify whether σ is an even or…

Q: The integers mod 5 (i.e., Z5) form a Boolean algebra, where - addition and multiplication are the…

A: The given question is solved below.

Q: Show that the permutations (12) and (12345) generate S5.

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Q: Exercise 3.1.18 State whether each of the following statements is true or false and give a brief…

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Q: Consider the following permutations in S7. ) 1234 567 1234567 3254617 2157463 (a) Write the…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: WIKS the largest order of an element in the groupof permutations of 4 objects!

A: What is the largest order of an element in the group of permutations of 4 objects

Q: Which of the following numbers could be the exact number ofelements of order 21 in a group: 21600,…

A: According to theorem, the number of elements of order n in a group is multiple of ϕ(n)

Q: Assume that n > 2 and x E A is a fixed element. How many unordered selections without repeats of k…

A: N>2, X is the element A is a fixed element  How many unordered selections withouts repeats of  k…

Q: Find the number of inversions in the permutation 436215.

A: The permutation given is 436215. To determine the number of inversion in the permutation 436215. The…

Q: Let n∈Z. Prove that n3−7n+18 is divisible by 6 for every interger n. Do not use induction.

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Q: 2. Let Qn be the number of permutations of {1,2, .., n} in which none of the patterns 12, 23, .., (n…

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Q: Find the solution to the recurrence relation an 3an 1+ 10an 2 with initial terms ao 10 and a, = 11.…

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Q: Consider the following permutations in S9 1 2 3 O = 4 5 6 7 1 2 3 4 5 6 7 8 9 89 and t = 3 5 1 4 69…

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Q: Let o be a fixed odd permutation in Sn. Show that every odd permutation in Sn can be written as a…

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Q: 5. Consider the following elements of A (1,2, 3,4, 5, 6, 7), (1,2, 3, 6, 5, 4, 7) (3,7,8). (2,5,…

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Q: 9. Use the algorithm to generate the next 22 permutations of {1,2,3,4,5} starting with 13275.

A: Given: A permuation {1, 2, 3, 4, 5} The algorithm for generating permutation follows an increasing…

Q: Suppose that " is in lowest terms and that m< n. Then has a simple-periodic dec- imal representation…

A: Introduction: The ratio of given two numbers could be represented as a factor less than one always…

Q: The product of an even number of disjoint cyclic is an even permutation

A: True

Q: - Let 1 2 3 4 5 6 7 8 2 3 5 6 7 1 8 4 1 2 3 4 5 6 7 8 4 8 3 6 1 2 5 7 and be permutations on the set…

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Q: 4. Write the permutation (6 5 7 9 2 1 4 8 (1 2 3 4 5 6 7 8 9. 10 as a product of disjoint cycles 10…

A: A permutation is a kind of arrangement of set of objects in order. To obtain the disjoint cycles,…

Q: аn — ар-1 +2а,-2 — п*, with ag 3D 1, aj %3D1.

A: We have to find Total Solution of given Recurrence relation.

Q: Consider the permutation T = (taqgblvxh)(n sk w fue)(ycodjr)(pzmi). (a) Showing your working, and…

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Q: Let n E N and let (b2n-1·· bo)2 be a binary representation of a natural number. Use induction to…

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Q: Consider all n! permutations of the set {1,2,3,..., n}. We say that a number i is a fixed point of a…

A: Given: pn(k) be number of permutations of 1, 2, ..., n that has exactly k fixed points.

Q: Consider the permutation 12345\/12345\/12345 31524 24153 45312 Express as a product of disjoint…

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Q: Obtain the generating function for the number of k-part compositions of n in which the ith part does…

A: Solution :-

Q: How many permutations of{1,2, . . . ,8}are there in which no even integer is a fixed point

A: We will permutations to find our required result.

Q: 7. Find a gcd of 49,349 and 15,555 in Z.

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