Understanding the Parity and Order of Permutations

  • Thread starter Thread starter wakko101
  • Start date Start date
  • Tags Tags
    Permutation
Click For Summary
The parity of a permutation indicates whether it is even or odd, and this is related to the order of the permutation, which refers to the cycle lengths. Specifically, a two-cycle is classified as odd, while a three-cycle is classified as even. The relationship between the parity and the order of permutations is significant in understanding their properties. Clarification on what is meant by "order" is essential for accurate interpretation. Understanding these concepts is crucial for deeper insights into permutation theory.
wakko101
Messages
61
Reaction score
0
I'm a bit confused about something. Does the parity of a permutation (i.e. if it is even or odd) tell you if the order of the permutation is even or odd, or are they unrelated?

Any insight would be appreciated.

Cheers,
W. =)
 
Physics news on Phys.org
What are you calling the order of a permutation? The order of the cycle length? If so, then yes, they are related. A two cycle is odd. A three cycle is even. Etc.
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
View full post »

Similar threads

Parity of Permutations: Understanding Even and Odd Cycles
  • · Replies 4 ·
Replies
4
Views
3K
Algebra and Permutations: Determining the Parity of an Element in S_n
  • · Replies 2 ·
Replies
2
Views
2K
Number of permutations to obtain identity
  • · Replies 1 ·
Replies
1
Views
3K
Linear Algebra / Linear Maps (Transformations)
  • · Replies 2 ·
Replies
2
Views
2K
Solving Permutation Groups: Odd Permutations Have Even Order
  • · Replies 3 ·
Replies
3
Views
3K
Permutations (with repetitions) problem
  • · Replies 5 ·
Replies
5
Views
2K
Prove that the order of An is (1/2)n
  • · Replies 16 ·
Replies
16
Views
4K
What is the parity inversion of antisymmetric tensor
  • · Replies 2 ·
Replies
2
Views
2K
Need help finding permutation matrix
  • · Replies 2 ·
Replies
2
Views
3K
Differing first-principle models for Maxwell-Boltzmann statistics?
  • · Replies 44 ·
2
Replies
44
Views
4K