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Results tagged with symmetric-groups
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user 11877
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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2
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A question about set of inversion
Let $w \in S_n$ and $inv(w) = \{(i,j): i,j \in \{1,\ldots,n\}, i<j, w(i)>w(j)\}$ the inversion set of $w$. Let ${\bf i}=(i_1,\ldots,i_m)$ be a sequence such that $s_{i_1}\cdots s_{i_m}$ is a reduced e …
- 6,201
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Factorization in the group algebra of symmetric groups
Let $S_n$ be the symmetric group on $\{1, \ldots, n\}$. Let
\begin{align}
T=\sum_{g\in S_n} g.
\end{align}
Are there some references about the factorization of $T$?
In the case of $n=3$, we have
\b …
- 17k