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New posts in permutation-cycles
Elements of $S_n$ can be written as a product of $k$-cycles.
abstract-algebra
group-theory
permutations
symmetric-groups
permutation-cycles
A little confusion regarding Sylow $p$-subgroups generated by a $p$-cycle
group-theory
sylow-theory
permutation-cycles
Why do the triangular numbers initially form long cycles mod $2^k$?
elementary-number-theory
permutations
modular-arithmetic
permutation-cycles
triangular-numbers
Number of homomorphisms between two arbitrary groups
abstract-algebra
group-theory
finite-groups
group-homomorphism
permutation-cycles
Why $c_1 ^{\omicron(\sigma)} = c_1 \implies c_1(\tau _1) = \tau_1 $ etc.
abstract-algebra
group-theory
permutation-cycles
Permutation group sending even to even and odd to odd
group-theory
permutations
symmetric-groups
permutation-cycles
parity
proving how many permutations exist.
combinatorics
permutation-cycles
How do you determine the characteristic polynomial of a permutation matrix based on the cycle type of the corresponding permutation??
linear-algebra
abstract-algebra
matrices
permutation-cycles
permutation-matrices
Sylow 2 subgroups of S4
group-theory
sylow-theory
permutation-cycles
Stabilizers in a permutation group
abstract-algebra
group-theory
permutations
group-actions
permutation-cycles
What are the properties of eigenvalues of permutation matrices?
linear-algebra
matrices
eigenvalues-eigenvectors
permutation-cycles
permutation-matrices
Simple expression for the joint orbit of two permutations
group-theory
permutations
permutation-cycles
Why are Stirling numbers of the first kind related to the number of permutations with $k$ cycles?
combinatorics
permutations
generating-functions
stirling-numbers
permutation-cycles
How to find the square root of a permutation
permutations
permutation-cycles
Suppose $n\geq 3$ and let $k$ be $n$ or $n-1$, whichever is odd. Show that the set of $k$-cycles in $A_n$ is not a conjugacy class in $A_n$.
abstract-algebra
group-theory
permutation-cycles
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