Newbetuts

Proving the number of even and odd permutations of a subgroup $H<S_{n}$ are equal, provided $H$ is not contained in $A_{n}$

Span of permutation matrices

An automorphism that has no fixed points except for the identity and is its own inverse implies commutativity

Show the centralisers $C_{S_6}(s)$ and $C_{S_6}(t)$ are isomorphic to $S_{3} \times C_{3}$

Other proofs that subgroups of $A_5$ have order at most 12

Let $H$ be a subgroup of $G$, and suppose that $G$ acts by multiplication over the set $X:=G/H$ of the left-hand side classes of $H$ over $G$.

Permutation of points $P_i\in X$ such that $\sum^n_{j=1}|P_{\sigma(j+1)}-P_{\sigma(j)}|^2\leq 8$

What is the total number of combinations such that a $6$-digit pin contains exactly $4$ distinct digits?

If $σ ∈ S_n$ is a cycle of odd order $m$, show that $σ^2$ is also a cycle of the same order $m$

Logic for decomposing a permutation into different products composed of transpositions

How do i prove how $S_5$ is generated by a two cycle and a five cycle?

For any set of numbers $1$ through $n$, what is the average probability that two randomly selected derangements are derangements of each other?

Is the sum of permutations of disjointed sets larger than the count of permutations in their union?

Permutations in a necklace with repeated beads

Finding the "square root" of a permutation

How many ways can the average of n dice be a?

New posts in permutations

Characterisation of the squares of the symmetric group

Simplify $\sum_{i=0}^n (i+1)\binom ni$

Bubble sorting question

Permutations on word $MISSISSIPPI$.

Proving the number of even and odd permutations of a subgroup $H<S_{n}$ are equal, provided $H$ is not contained in $A_{n}$

Span of permutation matrices

An automorphism that has no fixed points except for the identity and is its own inverse implies commutativity

Show the centralisers $C_{S_6}(s)$ and $C_{S_6}(t)$ are isomorphic to $S_{3} \times C_{3}$

Other proofs that subgroups of $A_5$ have order at most 12

Let $H$ be a subgroup of $G$, and suppose that $G$ acts by multiplication over the set $X:=G/H$ of the left-hand side classes of $H$ over $G$.

Permutation of points $P_i\in X$ such that $\sum^n_{j=1}|P_{\sigma(j+1)}-P_{\sigma(j)}|^2\leq 8$

What is the total number of combinations such that a $6$-digit pin contains exactly $4$ distinct digits?

If $σ ∈ S_n$ is a cycle of odd order $m$, show that $σ^2$ is also a cycle of the same order $m$

Logic for decomposing a permutation into different products composed of transpositions

How do i prove how $S_5$ is generated by a two cycle and a five cycle?

For any set of numbers $1$ through $n$, what is the average probability that two randomly selected derangements are derangements of each other?

Is the sum of permutations of disjointed sets larger than the count of permutations in their union?

Permutations in a necklace with repeated beads

Finding the "square root" of a permutation

How many ways can the average of n dice be a?