All Questions
Tagged with integer-partitions symmetric-groups
21
questions
6
votes
1
answer
196
views
Flattening Young Tableaux
Let $\lambda=(\lambda_1,\lambda_2,\cdots,\lambda_k)$ be a partition with $|\lambda|=n$ and $\lambda_1\geq \lambda_2\geq\cdots\geq \lambda_k$. For any Standard Young Tableaux (SYT) $T$ of shape $\...
- 32.9k
5
votes
0
answers
284
views
On Applications of the Murnaghan-Nakayama rule
The question is located below. In short, I am looking for an accessible explanation of the Murnaghan-Nakayama rule in relation to the following problem. Pardon the long setup.
Let $Y$ be a standard ...
- 32.9k
3
votes
1
answer
111
views
Symmetry of Plancherel measure (for $S_n$)
For each $n \geq 1$ consider the reverse lexicographical order on the set $P(n)$ of partitions of $n$. Example for $n=7$:
$$
\begin{pmatrix}
\hline
1 & 2 & 3 & 4 & 5 & 6 & 7 ...
- 2,052
8
votes
1
answer
742
views
Characters of the symmetric group corresponding to partitions into two parts
Let $n\in\mathbb N$ be a natural number and $\lambda=(a,b)\vdash n$ a partition of $n$ into two parts, i.e. $a\ge b$ and $a+b=n$. In this special case, is there a simple description of the character $\...
user38451
6
votes
0
answers
445
views
Invariant element in the tensor product of rectangular Specht modules?
Denote by $\mathfrak{S}_k$ the symmetric group on $k$ elements. Let $\lambda=(n^2\times n)=(n^2,\ldots,n^2)$ be a rectangular partition and $k=n^3$. Denote by $S_\lambda$ the Specht module ...
- 14.9k
15
votes
2
answers
373
views
A question on partitions of n
Let $P$ be the set of partitions of $n$. Let $\lambda$ denote the shape of a particular partition. Let $f_\lambda(i)$ be the frequency of $i$ in $\lambda$ and let $a_\lambda(i) := \# \lbrace j : f_\...
- 228