Let's start with some family of algebraic structures of the same type indexed by the natural numbers, say the symmetric group $S_n$. Suppose that the axioms of this algebraic structure (in this case, ...
Background For $\lambda$ any partition and $n$ a positive integer, write $\lambda[n]$ for the sequence $(n - |\lambda|, \lambda_1, \lambda_2, \ldots, \lambda_r)$. For $n$ large enough, this is a ...
I've gotten stuck in a project I have been working on, essentially on the following combinatorial question about the symmetric group. One can obtain a 1-dimensional representation $M^n_c$ of the ...
The automorphism group of the symmetric group $S_n$ is $S_n$ when $n$ is not $2$ or $6$, in which cases it is respectively $1$ and the semidirect product of $S_6$ with the (cyclic) group of order $2$. ...