Newbetuts

Prove that the order of an element in $S_n$ equals the least common multiple of the lengths of the cycles in its cycle decomposition.

Bruteforcing a keypad lock

Arrangements of a,a,a,b,b,b,c,c,c in which no three consecutive letters are the same

Why is $S_5$ generated by any combination of a transposition and a 5-cycle?

Exponential Generating Function For Derangements

Index of a permutation that has repetition [closed]

Sitting Chair problem with 5 boys and 6 girls with restrictions

$G\le S_n$ in which all $g\ne e$ have $<\sqrt{n}$ cycles must be $\Bbb Z_p$ or $\Bbb Z_p\rtimes\Bbb Z_q$

Existence of subgroup of order six in $A_4$

Can $G≅H$ and $G≇H$ in two different views?

Derivation of the Partial Derangement (Rencontres numbers) formula

How many permutations of 11 elements are there, from a set of 12 elements with $3$ a's, $3$ b's, $3$ c's, and $3$ d's?

Counting all possibilities that contain a substring

How many permutations of $\{1,2,3,...,n\}$ there are with no 2 consecutive numbers?

How many elements of order $k$ are in $S_n$?

New posts in permutations

Calculating the number of possible paths through some squares

Six Frogs - Puzzle (order reversal using special transpositions)

"In a party people shake hands with one another"

Show that : $\sum\limits_{\sigma \in S_n} (\mbox{number of fixed points of } \sigma)^2= 2 n!$

Row swap changing sign of determinant

Prove that the order of an element in $S_n$ equals the least common multiple of the lengths of the cycles in its cycle decomposition.

Bruteforcing a keypad lock

Arrangements of a,a,a,b,b,b,c,c,c in which no three consecutive letters are the same

Why is $S_5$ generated by any combination of a transposition and a 5-cycle?

Exponential Generating Function For Derangements

Index of a permutation that has repetition [closed]

Sitting Chair problem with 5 boys and 6 girls with restrictions

$G\le S_n$ in which all $g\ne e$ have $<\sqrt{n}$ cycles must be $\Bbb Z_p$ or $\Bbb Z_p\rtimes\Bbb Z_q$

Existence of subgroup of order six in $A_4$

Can $G≅H$ and $G≇H$ in two different views?

Derivation of the Partial Derangement (Rencontres numbers) formula

How many permutations of 11 elements are there, from a set of 12 elements with $3$ a's, $3$ b's, $3$ c's, and $3$ d's?

Counting all possibilities that contain a substring

How many permutations of $\{1,2,3,...,n\}$ there are with no 2 consecutive numbers?

How many elements of order $k$ are in $S_n$?