Richard Stanley through a crystal lens and from a random angle

  title={Richard Stanley through a crystal lens and from a random angle},
  author={A. Schilling},
  journal={arXiv: Combinatorics},
  • A. Schilling
  • Published 2014
  • Mathematics
  • arXiv: Combinatorics
  • 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

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