# Questions tagged [symmetric-groups]

The symmetric group $S_n$ is the group of permutations of the set of integers $\{1,\dots,n\}$. This has $n!$ elements and is generated by the $n-1$ involutions exchanging consecutive integers. The symmetric groups form the simplest family of Coxeter groups.

**2**

**0**answers

### Upper bound on decomposition numbers for the symmetric group in a block of weight $w$

**2**

**0**answers

### Involutive solutions to the Yang-Baxter equation (and triangular Hopf algebras)

**10**

**1**answer

### When are immanants irreducible?

**11**

**0**answers

### Hidden grading on $kS_n$

**0**

**0**answers

### Greatest common length of permutation

**3**

**2**answers

### Is there any simple formula for the character of $S_{n}$ represented by the set of $k$-tuples of $\{1,2,…,n\}$?

**9**

**7**answers

### Representations of products of symmetric groups

**3**

**1**answer

### What is the $p$-regular partition corresponding to the sign representation of $S_{n}$ over a field of characteristic $p$?

**7**

**1**answer

### Hurwitz numbers and $t$-cores

**2**

**1**answer

### Changing $S_2 \wr S_n$ for $S_n \wr S_2$ in the theory of zonal polynomials

**1**

**0**answers

### On the real and finite field rank of a $0/1$ matrix - II

**4**

**1**answer

### A close reative of “Inflated” Eulerian polynomials

**3**

**0**answers

### Reference for the Netto's theorem on the permutation groups which was mentioned in the paper of Frobenius

**1**

**0**answers

### Irreducible representation of transposed Young diagram of $\mathfrak{S}_n$ [closed]

**7**

**1**answer

### For which $n$ can $S_n$ act transitively on $n+k$ elements?

**10**

**2**answers

### Arbitrarily large finite irreducible matrix groups in odd dimension?

**1**

**0**answers

### Is there any research on the action of a subgroup on the whole finite group by conjugation?

**2**

**1**answer

### Combinatorial problem in $\mathsf{S}_4$

**2**

**0**answers

### Finding the decorated permutation of a non-reduced plabic graph

**3**

**0**answers

### Faithful representation into $\operatorname{GL}(9,3)$

**4**

**1**answer

### I want to know the name of or any references for a matrix in the book “The representation theory of the symmetric groups” by Gordon James

**8**

**0**answers

### A question related to Young symmetrizers

**6**

**0**answers

### Classification of posets that are quotient posets of the Boolean lattice

**3**

**1**answer

### A basic question about Young symmetrizers

**5**

**1**answer

### On a certain expansion in term of Schur functions

**8**

**0**answers

### Generalized Young symmetrizers, why not?

**3**

**1**answer

### Permutation representation of a finite $p$-group

**4**

**0**answers

### Words that give rise to an enumeration of elements of the symmetric group

**4**

**0**answers

### Question about generalizing Cauchy identity

**4**

**1**answer

### Number of paths in the Bruhat order in the symmetric group

**7**

**0**answers

### A question regarding an analog of Young symmetrizer: the product row and column preserving subgroups without sign representation

**3**

**0**answers

### Consequences of Littlewood-Richardson rule

**3**

**0**answers

### Character table of the symmetric group $S_n$ according to James

**3**

**0**answers

### Suggested papers or reading for PDE (high dimension) reduction to ODE by symmetries

**4**

**1**answer

### Reduce PDE to ODE by dilation symmetry

**8**

**1**answer

### Induction step in Bóna and Ehrenborg's proof that the generating function of the alternating runs has -1 as a root of a certain multiplicity

**9**

**2**answers

### Decomposing a polynomial ring into Specht Modules

**3**

**1**answer

### action of symmetric group on the second exterior power

**5**

**2**answers

### Transposition Cayley graphs are planar

**2**

**1**answer

### Recurrence relation for number of reduced words of longest element in $S_n$

**2**

**0**answers

### Carter Payne homomorphisms and reduced expressions

**2**

**0**answers

### Expansion of polytabloids in the standard basis

**-1**

**1**answer

### On bounding a certain discrepancy between probability distributions on the symmetric group

**3**

**0**answers

### Sum of products of irreducible characters of the symmetric group over a subgroup

**1**

**0**answers

### Combinatorial bijection on monotone sequences

**1**

**0**answers

### Singular chain complex of balanced products

**7**

**2**answers

### What makes skew characters of the symmetric group special?

**7**

**0**answers

### Non-zero group determinant for symmetric group

**2**

**0**answers

### CAS for finite-dimensional complex representations of $S_n$

**2**

**1**answer