All Questions
Tagged with young-tableaux reference-request
10
questions
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Normalizer of a Young subgroup in symmetric group
In $S_n$, a Young subgroup $S_{r_1}^{m_1}\times S_{r_2}^{m_2}\times ... S_{r_k}^{m_k}$ where $m_1\times r_1+...+m_k\times r_k=n$ has normalizer $N=S_{r_1}wr S_{m_1} \times ...\times S_{r_k}wr S_{m_k}$....
- 1,303
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38
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Does this partial order on semistandard Young tableaux have a name?
Given a semistandard Young tableau $T$ of shape $\lambda$, let $c_i(T)$ is the number of $i$'s that appear in $T$. We can define a partial order on the set of all semistandard Young tableau of some ...
- 437
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Bijection between noncrossing sets of arcs and row-strict Young tableaux
There is a well-known bijection between (i) noncrossing partitions of the set {1,...,2n} where all blocks have size 2, and (ii) standard Young tableaux with n rows and 2 columns. There exist a Catalan ...
- 67
2
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Reference for Identities of Young Symmetrizers
Considering Young Tableaux filled with numbers $1,...,n$ in a natural way, (left-to-right, row-by-row), the book "Representation Theory" of Fulton and Harris (Exercise 4.24) states that for all $x$ in ...
- 292
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LR-rule and Standard Young Tableau counting
given that $s_\lambda s_\mu=\sum_{\nu} C_{\lambda \mu}^\nu s_\nu$ with $\vert \lambda\vert +\vert\mu \vert=\vert \nu\vert$, why does apparently also hold that $$h(\lambda) h(\mu) {\vert \nu\vert \...
- 910
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505
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Counting the number of semistandard Young Tableaux with maximum entry $n.$ Reference/Formula request
Question: If $k \leq n$ let $\lambda_k$ be a Young diagram with square $k \times k$ shape. I write $\#_{\lambda_{k}^n}$ to count the
number of semistandard Young tableaux with shape $\lambda_k$ and
...
- 3,788
4
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2
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736
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Reference request: Representation theory over fields of characteristic zero
Many representation theory textbooks and online resources work with the field of complex numbers or more generally algebraically closed fields of characteristic zero. I am looking for a good textbook ...
- 2,584
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Non-Intersecting up-right lattice paths and standard Young Tableaux
Consider the Lattice $\mathbb{Z}^2$ and an initial set of points with coordinates $(0,u_1)$, $(0,u_2)$, $\cdots$ $(0,u_n)$, final set of points $(m,v_1),(m,v_2),\cdots,(m,v_n)$, where $v_i,u_i$ are ...
- 32.9k
4
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1
answer
155
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Bounds on Young Tableau Element locations
I'm having trouble finding some elementary results on the following. Let $Y$ be a standard Young Tableau of shape $\lambda=(\lambda_1,\lambda_2,\ldots,\lambda_n)$ with $N:=\sum_{i=1}^n\lambda_i$.
My ...
- 32.9k
8
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1
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Historical reference request: Young tableaux
I am writing up an article on the RSK correspondence. To this end, I want to understand the history behind the invention of the Young tableaux and how it was introduced into the study of the symmetry ...
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