Is there a formula or way to determine how many transpositions there are for a cycle of a given length? Is there a bound of sorts on the minimum and maximum number of transpositions for a cycle of a given length? For example, suppose I have a cycle of length 5. I know there are only an even number of transpositions possible, but how many are there actually? Wouldn't the smallest number be 4 transpositions for a cycle of length 5? I know there is one with 6 transpositions possible for a cycle of length 5? Are there others? If so, can we determine them? Is it correct to say that if a permutation is a 5-cycle, then it has 2s number of possible transpositions?
Is there a formula or way to determine how many transpositions there are for a cycle of a given length? Is there a bound of sorts on the minimum and maximum number of transpositions for a cycle of a given length? For example, suppose I have a cycle of length 5. I know there are only an even number of transpositions possible, but how many are there actually? Wouldn't the smallest number be 4 transpositions for a cycle of length 5? I know there is one with 6 transpositions possible for a cycle of length 5? Are there others? If so, can we determine them? Is it correct to say that if a permutation is a 5-cycle, then it has 2s number of possible transpositions?
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.7: Introduction To Coding Theory (optional)
Problem 12E: Suppose that the check digit is computed as described in Example . Prove that transposition errors...
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Is there a formula or way to determine how many transpositions there are for a cycle of a given length? Is there a bound of sorts on the minimum and maximum number of transpositions for a cycle of a given length? For example, suppose I have a cycle of length 5. I know there are only an even number of transpositions possible, but how many are there actually? Wouldn't the smallest number be 4 transpositions for a cycle of length 5? I know there is one with 6 transpositions possible for a cycle of length 5? Are there others? If so, can we determine them? Is it correct to say that if a permutation is a 5-cycle, then it has 2s number of possible transpositions?
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