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A survey of reduced decompositions of permutations
Special Events| Speaker: | Richard P. Stanley, Applied Mathematics MIT |
| Location: | 1147 MSB |
| Start time: | Tue, Jan 17 2012, 3:10PM |
Description
Abstract (in LaTeX): Let $s_i$ denote the adjacent transposition
$(i,i+1)\in\mathfrak{S}_n$ (the symmetric group on $\{1,2,\dots,n\}$),
$1\leq i\leq n-1$. A \emph{reduced decomposition} of a permutation
$w\in\mathfrak{S}_n$ is a sequence $(b_1,\dots,b_p)$ for which
$w=s_{b_1}\cdots s_{b_p}$ and $p$ is minimal. A basic combinatorial
problem is to determine the number $r(w)$ of reduced decompositions of
$w$. This problem leads to a rich theory involving Young tableaux,
symmetric functions, a version of the RSK-algorithm, Schubert
polynomials, Schur and Weyl modules, flag varieties, etc.