Questions tagged [robinson-schensted-knuth]

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RSK on matrices with non-integer values

In the usual RSK algorithm, matrices with non-negative integer valued entries are mapped bijectively to a pair of tableaux. The length of the top row of either of the tableaux gives the maximal weight ...
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Let $W(B_n)$ be a Weyl group of type $B_n$ and $SBT (n)$ the set of standard bitableaux of size $n$. Similar to Robinson-Schensted correspondences, I know that there exists a map $W(B_n) \to SBT (n) \... 0answers 325 views Staircase Schur functions squared Let$\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$is the Schur function indexed by ... 2answers 445 views Dynamics of RSK There is a way of viewing the RSK correspondence as a map (in fact, bijection)$A \overset{RSK}\longrightarrow \widehat{A}$from$n\times n$matrices with entries$\mathbb{N}$to (weak) reverse plane ... 0answers 130 views Degeneration of modules over the affine symmetric group and jeu de taquin Let$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$... 2answers 1k views Has Reifegerste's Theorem on RSK and Knuth relations received a slick proof by now? For the notations I am using, I refer to the Appendix at the end of this post. Here is what, for the sake of this post, I consider to be Reifegerste's theorem: Theorem 1. Let$n\in\mathbb N$and$i\...
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 $1,\dots,n$...