Given a permutation, how to calculate the number of nonidentity odd cycles of it?












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







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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
















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







share|cite|improve this question











$endgroup$












  • $begingroup$
    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














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







share|cite|improve this question











$endgroup$




$sigma$ 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






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Feb 1 at 5:15







water graph

















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


















  • $begingroup$
    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










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