Write a permutation as a product of disjoint cycles

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Christian Lawson-Perfect

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Christian Lawson-Perfect 4 years, 8 months ago

Gave some feedback: Ready to use

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Bill Foster 6 years, 6 months ago

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Newcastle University Mathematics and Statistics 9 years, 2 months ago

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Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

perms	list	List of 4 items
prod	permutation	perm("(2,5,4)")
n	integer	5

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
repeat(perm(randomcycle(n)),4)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `list`

[ perm("(1,4,3,5,2)"), perm("(1,2,3,4,5)"), perm("(1,5)"), perm("(1,5)") ]

← Depends on:

→ Used by:

prod

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"Unnamed part" - prompt

Parts

Write a permutation in cycle notation

Write a permutation in cycle notation

Ask the student a question, and give any hints about how they should answer this part.

Write as a product of disjoint cycles

$\var{perms[0]} \var{perms[1]} \var{perms[2]} \var{perms[3]}$

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Correct answer

xxxxxxxxxx
 
prod

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Must the cycles be disjoint?

Must the cycles be transpositions?

Name of the identity permutation

The student should write this string for the identity permutation.

Advice

Each set of brackets represents a cycle, with each number being mapped to the one on its right, and the last number in the sequence mapped to the first.

Follow each number through the cycles, starting with the rightmost cycle and reading leftwards. For example, here's how $1$ is mapped to $\var{prod[1]}$:

\[ \var{latex(tracemap(1,perms))} \]

Then repeat this for $\var{prod[1]}$, until you get back to $1$. This is a single cycle. If any number is not included in this cycle, repeat this process starting at that number to get another, disjoint, cycle. Some numbers are mapped to themselves - these are trivial cycles and you don't need to write them down. Once you've covered every number, you should have the following:

\[ \var{prod} \]

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Write a permutation in cycle notation
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Write a permutation as a product of disjoint cycles

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Taxonomy: mathcentre

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Taxonomy: Context

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Checkpoint description

Christian Lawson-Perfect 4 years, 8 months ago

Bill Foster 6 years, 6 months ago

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Write a permutation in cycle notation

Loading...

Error

Write a permutation as a product of disjoint cycles

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 4 years, 8 months ago

Bill Foster 6 years, 6 months ago

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Write a permutation in cycle notation

Generated value: `list`