G. Consider the permutation (1 3 5 4 2)(1 4 3 5).1. Express as a product of disjoint cycles.2. What is the order of the given permutation?3. Express your answer in number 1 as a product of transpositions.4. Determine whether the permutation is even or odd.

Answered: G. Consider the permutation (1 3 5 4…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 52E

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Similar questions

Answer the following questions. 4. Describe how the permutation of ii objects differs from the permutation of choosing r objects from a set of n objects. Include how each is calculated.
True or False Label each of the following statements as either true or false. 6. Every permutation can be expressed as a product of disjoint cycles.
One advantage of decomposing a permutation as a product of disjoint cycles is that disjoint cycles commute. To verify this, let a = {a1, a2, ...., ak} and b = {b1,b2, ...., bm} be disjoint cycles in Sn. Show that (ab)(t) = (ba)(t) for every t ∈ {1,2,..., n} by considering cases.
Suppose a permutation s swaps the ﬁrst two elements of {1, 2, ..., n}. A permutation r rotates the elements: r(1)=2, r(2)=3, ... r(n-1)=n, r(n)=1. We can thus write in cycle notation: s=(1 2), r=(1 2 3 4 ... n). What does the permutation rm sr -m do?
Let σ = (1,2,3)(2,3,4,5). (a) Write σ as a multiplication of disjoint cycles. (b) Write σ as a multiplication of transpositions. (c) Is σ even or odd?
b, c, a, or no generator, since it is not cyclic?
b. Determine whether the following given permutation is even or odd? (picture)

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G. Consider the permutation (1 3 5 4 2)(1 4 3 5). 1. Express as a product of disjoint cycles. 2. What is the order of the given permutation? 3. Express your answer in number 1 as a product of transpositions. 4. Determine whether the permutation is even or odd.