Richard Stanley through a crystal lens and from a random angle

@article{Schilling2014RichardST,
title={Richard Stanley through a crystal lens and from a random angle},
author={A. Schilling},
journal={arXiv: Combinatorics},
year={2014}
}

We review Stanley's seminal work on the number of reduced words of the longest
element of the symmetric group and his Stanley symmetric functions. We shed new light on
this by giving a crystal theoretic interpretation in terms of decreasing factorizations of
permutations. Whereas crystal operators on tableaux are coplactic operators, the crystal
operators on decreasing factorization intertwine with the Edelman-Greene insertion. We also
view this from a random perspective and study a Markov… CONTINUE READING