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New posts in permutations
The pigeonhole principle and a professor who knows $9$ jokes and tells $3$ jokes per lecture
combinatorics
permutations
combinations
pigeonhole-principle
If the number of triplet $(l,m,n)$ satisfying $1\leq l\leq m\leq n \leq 20$ is $p \choose q$ then least value of $p+q$ is?
combinatorics
permutations
combinations
The transpose of a permutation matrix is its inverse.
linear-algebra
abstract-algebra
matrices
permutations
permutation-matrices
What is $\tau(A_n)$?
abstract-algebra
group-theory
finite-groups
permutations
additive-combinatorics
How does one compute the sign of a permutation?
group-theory
algorithms
permutations
finite-groups
Why is the determinant defined in terms of permutations?
linear-algebra
matrices
permutations
definition
determinant
Odd/Even Permutations
abstract-algebra
discrete-mathematics
permutations
How to find the square root of a permutation
permutations
permutation-cycles
What is the shortest string that contains all permutations of an alphabet?
combinatorics
permutations
Can someone explain Cayley's Theorem step by step?
abstract-algebra
group-theory
finite-groups
permutations
symmetric-groups
Show group of order $4n + 2$ has a subgroup of index 2.
abstract-algebra
group-theory
finite-groups
permutations
$(12)$ and $(123\dots n)$ are generators of $S_n$
abstract-algebra
group-theory
permutations
finite-groups
symmetric-groups
Counting number of moves on a grid
combinatorics
discrete-mathematics
permutations
How many 7-note musical scales are possible within the 12-note system?
combinatorics
permutations
combinations
music-theory
How to write permutations as product of disjoint cycles and transpositions
abstract-algebra
permutations
$A_4$ has no subgroup of order $6$?
abstract-algebra
group-theory
finite-groups
permutations
symmetric-groups
Find the center of the symmetry group $S_n$.
abstract-algebra
group-theory
permutations
symmetric-groups
In how many ways can we choose a black square and a white square from a chessboard so that they are neither in the same row nor the same column
combinatorics
permutations
combinations
An epimorphism from $S_{4}$ to $S_{3}$ having the kernel isomorphic to Klein four-group
group-theory
permutations
finite-groups
epimorphisms
Multiplication in Permutation Groups Written in Cyclic Notation
abstract-algebra
group-theory
permutations
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