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Let $\Gamma$ be a Coxeter group on some generating set $S$, with reflection representation $V$. Then $\Gamma$ has two standard partial orders, the weak and strong Bruhat orders. Moreover, if $\lambda ... 1answer 679 views ### Bruhat order and the Robinson-Schensted correspondence The Robinson-Schensted correspondence is a bijection between elements of the symmetric group$S_n$and pairs of standard tableaux of the same shape. The symmetric group is partially ordered by the ... 3answers 578 views ### Kazhdan-Luzstig Polynomials and Lower Intervals in the Bruhat Order I have read in a number of places that the lower Bruhat interval$[e, w]$is rank-symmetric if and only if the KL-polynomial$P_{e, w}(q) = 1$. All of the proofs I've come across use "rationally ... 1answer 276 views ### Efficient enumeration of Bruhat intervals Hi everyone. I'm currently programming some stuff for Hecke algebras. My current implementations have several bottlenecks and I'd like to improve that as much as I can so that I can use stuff like$...
For those who are unfamiliar with the terminology, I'll explain a little. The symmetric group $S_n$, as a type A Coxeter group, has generators $\{s_1,\ldots,s_{n-1}\}$ with relations (1) $s_i^2$ for ...
Let $\pi\in S_n$. I recently needed to understand the permutations $\rho$ such that $\rho\not\leq\pi$ in Bruhat order. Since there are $O(n!)$ of those I really wanted a description of the $O(n^2)$ ...