Mixing
Given a permutation, how to calculate the number of nonidentity odd cycles of it?
0
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$sigma$ is a permutation on $n$ points and it can be written as a product of nonidentity cycles, how to calculate the number of odd nonidentity cycles in this product?
This number is congruent to $n; (mod;2)$.
linear-algebra permutations
asked Feb 1 at 3:46
water graphwater graph
425
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add a comment |
0
$begingroup$
$sigma$ is a permutation on $n$ points and it can be written as a product of nonidentity cycles, how to calculate the number of odd nonidentity cycles in this product?
This number is congruent to $n; (mod;2)$.
linear-algebra permutations
asked Feb 1 at 3:46
water graphwater graph
425
$endgroup$
$begingroup$
What does $i$ refer to?
$endgroup$
– saulspatz
Feb 1 at 4:24
$begingroup$
I have made a mistake, it should be $n$.
$endgroup$
– water graph
Feb 1 at 5:15
1
$begingroup$
I don't understand the question. Every permutation can be written as the product of disjoint cycles in an essentially unique way. Do you have a specific permutation $sigma$ in mind, or are you looking for some kind of general statement? If the latter, what would be the answer you're looking for in the case $n=3?$
$endgroup$
– saulspatz
Feb 1 at 5:23
add a comment |
0
0
0
$begingroup$
$sigma$ is a permutation on $n$ points and it can be written as a product of nonidentity cycles, how to calculate the number of odd nonidentity cycles in this product?
This number is congruent to $n; (mod;2)$.
linear-algebra permutations
asked Feb 1 at 3:46
water graphwater graph
425
$endgroup$
$sigma$ is a permutation on $n$ points and it can be written as a product of nonidentity cycles, how to calculate the number of odd nonidentity cycles in this product?
This number is congruent to $n; (mod;2)$.
linear-algebra permutations
linear-algebra permutations
asked Feb 1 at 3:46
water graphwater graph
425
asked Feb 1 at 3:46
water graphwater graph
425
edited Feb 1 at 5:15
water graph
asked Feb 1 at 3:46
water graphwater graph
425
asked Feb 1 at 3:46
water graphwater graph
425
asked Feb 1 at 3:46
water graphwater graph
425
425
$begingroup$
What does $i$ refer to?
$endgroup$
– saulspatz
Feb 1 at 4:24
$begingroup$
I have made a mistake, it should be $n$.
$endgroup$
– water graph
Feb 1 at 5:15
1
$begingroup$
I don't understand the question. Every permutation can be written as the product of disjoint cycles in an essentially unique way. Do you have a specific permutation $sigma$ in mind, or are you looking for some kind of general statement? If the latter, what would be the answer you're looking for in the case $n=3?$
$endgroup$
– saulspatz
Feb 1 at 5:23
add a comment |
$begingroup$
What does $i$ refer to?
$endgroup$
– saulspatz
Feb 1 at 4:24
$begingroup$
I have made a mistake, it should be $n$.
$endgroup$
– water graph
Feb 1 at 5:15
1
$begingroup$
I don't understand the question. Every permutation can be written as the product of disjoint cycles in an essentially unique way. Do you have a specific permutation $sigma$ in mind, or are you looking for some kind of general statement? If the latter, what would be the answer you're looking for in the case $n=3?$
$endgroup$
– saulspatz
Feb 1 at 5:23
$begingroup$
What does $i$ refer to?
$endgroup$
– saulspatz
Feb 1 at 4:24
$begingroup$
What does $i$ refer to?
$endgroup$
– saulspatz
Feb 1 at 4:24
$begingroup$
I have made a mistake, it should be $n$.
$endgroup$
– water graph
Feb 1 at 5:15
$begingroup$
I have made a mistake, it should be $n$.
$endgroup$
– water graph
Feb 1 at 5:15
1
1
$begingroup$
I don't understand the question. Every permutation can be written as the product of disjoint cycles in an essentially unique way. Do you have a specific permutation $sigma$ in mind, or are you looking for some kind of general statement? If the latter, what would be the answer you're looking for in the case $n=3?$
$endgroup$
– saulspatz
Feb 1 at 5:23
$begingroup$
I don't understand the question. Every permutation can be written as the product of disjoint cycles in an essentially unique way. Do you have a specific permutation $sigma$ in mind, or are you looking for some kind of general statement? If the latter, what would be the answer you're looking for in the case $n=3?$
$endgroup$
– saulspatz
Feb 1 at 5:23
add a comment |
0
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$begingroup$
What does $i$ refer to?
$endgroup$
– saulspatz
Feb 1 at 4:24
$begingroup$
I have made a mistake, it should be $n$.
$endgroup$
– water graph
Feb 1 at 5:15
1
$begingroup$
I don't understand the question. Every permutation can be written as the product of disjoint cycles in an essentially unique way. Do you have a specific permutation $sigma$ in mind, or are you looking for some kind of general statement? If the latter, what would be the answer you're looking for in the case $n=3?$
$endgroup$
– saulspatz
Feb 1 at 5:23