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6
votes
0answers
223 views

Staircase Schur functions squared

Let $\Delta_n$ be the staircase-shaped partition $(n-1,n-2,\dots,1)$. Are there any non-obvious combinatorial objects that index $s_{\Delta_n}^2$? Here, $s_\lambda$ is the Schur function indexed by ...
10
votes
1answer
304 views

Dynamics of RSK

There is a way of viewing the RSK correspondence as a map (in fact, bijection) $A \overset{RSK}\longrightarrow \widehat{A}$ from $n\times n$ matrices with entries $\mathbb{N}$ to (weak) reverse plane ...
4
votes
0answers
115 views

Degeneration of modules over the affine symmetric group and jeu de taquin

Let $H_n$ be the group algebra of the affine Coxeter group of type A (feel free to replace it by the affine Hecke algebra). This is generated by elements $y_i$'s, $i=1,\dots,n$ and transpositions $s_i$...
16
votes
2answers
1k views

Has Reifegerste's Theorem on RSK and Knuth relations received a slick proof by now?

For the notations I am using, I refer to the Appendix at the end of this post. Here is what, for the sake of this post, I consider to be Reifegerste's theorem: Theorem 1. Let $n\in\mathbb N$ and $i\...
7
votes
1answer
369 views

Does this lattice have a name (and literature)?

The "lattice" in the title appears to be a lattice. At least it's a poset, which I define now. Fix a partition $\lambda$ of $n$ and consider the set of all standard Young tableaux (each of $1,\dots,n$...
12
votes
3answers
638 views

Generalization's of Greene's Theorem for the Robinson-Schensted correspondence

One important property of the Robinson-Schensted correspondence (RS) is that the longest increasing subsequence of the permutation $\sigma$ is $\lambda_1$, the first entry of the shape $\lambda(\sigma)...
1
vote
0answers
139 views

What is the RSK correspondence for $G\wr S_n.$

What is the RSK correspondence for $G\wr S_n$?. Where can I read about this?
9
votes
2answers
460 views

Viennot-type geometric description for dual RSK correspondence?

Is a geometric construction of the dual RSK correspondence along the lines of Viennot's "light and shadows construction" written up somewhere? This is a bijective correspondence between 0-1 matrices ...
17
votes
1answer
678 views

Bruhat order and the Robinson-Schensted correspondence

The Robinson-Schensted correspondence is a bijection between elements of the symmetric group $S_n$ and pairs of standard tableaux of the same shape. The symmetric group is partially ordered by the ...
4
votes
3answers
640 views

RS to RSK correspondence

The RS correspondence is a correspondence which associates to each permutation a pair of standard Young tableaux of the same shape. The RSK correspondence associates to each integer matrix (with non-...
23
votes
1answer
518 views

Permutations, stopping times, Bessel functions, hook formula and Robinson-Schensted

For given counting number $n$, consider all permutations $\pi$ of {$1,\ldots,n$}, generate for every $\pi$ its Robinson-Schensted pair of standard tableaux $(P_\pi,Q_\pi)$ and average together all the ...