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.

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### The number of permutations with a special condition

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### The number of permutations with specified number of cycles and fixed points

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### Is this sum of cycles invertible in QSn?

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### Cycle generating function of permutations with only odd cycles

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### Ref. request: Enumerating elements of Bruhat cells

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### Combinatorics of $p$-Kazhdan--lusztig polynomials

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### Can $S_n$ be partitioned into subsets containing an involution and satisfying $∀σ≠τ, ∃j$ s.t. $σ(j)≠τ(j),σ^{−1}(j)=τ^{−1}(j)$?

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### Cycle Structure of a Permutation Based on the Binary Representation

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### Reference request: Coxeter length and irreducible characters

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### Character theoretic proof of the Littlewood–Richardson rule?

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### Combinatorial model for twisted involutions in $S_n$

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### Large subgroups of $S_n$ without large symmetric or alternating subgroups

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### working with symmetric groups presented via nonstandard generators

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### A dimension formula for generalised symmetric powers of the natural module

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### Permutation factorizations according to number of generated orbits

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### Homotopy type of the semi-simplicial set of symmetric groups

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### What are all the transitive extensions of cyclic groups?

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### Edge-transitive Cayley graphs of $S_n$

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### Tabloid Construction of Permutation Representation of Hyperoctahedral Group

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**1**answer

### Is the Normal centralizer problem in P?

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**3**answers

### Low-dimensional irreducible 2-modular representations of the symmetric group

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### Symmetric functions of eigenvalues

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### Number of permutations in a set in an algorithm

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### Murnaghan-Nakayama rule when all cycles have same size

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**1**answer

### Dimension of irreducible representation associated to a Young tableau

**7**

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### Upper bound on the number of permutations in a set during an algorithm

**7**

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### Generating symmetric groups with small cycles

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**0**answers

### Natural maps between Schur functors: understanding the image

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**2**answers

### alternating and symmetric powers of the standard representation of the symmetric group

**11**

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### Question on a reduction in Kirillov's paper on positivity of divided difference operators

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### Characterization of permutations which have at most one successor in the covering relation of the weak Bruhat order

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### Generating sets of the symmetric group that yield isomorphic Cayley graphs

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### A question about set of inversion

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### Permanent of the symmetric group

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**1**answer

### The number of permutations of a given cycle type that fix a string with a given histogram

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### Induced representation of a Young subgroup

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### Classification of transitive subgroups of finite symmetric groups generated by double transpositions

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### Character values at a cyclic permutation of a symmetric group

**11**

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### Bijective proof of an identity involving number of standard Young tableaux and semistandard tableaux

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**1**answer

### Reference request: Reduced reflection length in Coxeter groups

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**2**answers

### Provoking involutions further

**16**

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### Irreducible representations occuring in $\mathrm{Ind}_G^{S_{|G|}}1$ for $G$ finite group

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### A constraint satisfaction problem on matrix sum involving symmetric group

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### What is this symmetric simplex category, concretely?

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### trace and involution permutations: Part II

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### trace and involution permutations: Part I

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### hooks and contents: Part II

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### hooks and contents: Part I

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### Solutions of $x^d=1$ in the symmetric group

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