Consequences of the Lakshmibai-Sandhya Theorem: the ubiquity of permutation patterns in Schubert calculus and related geometry

  title={Consequences of the Lakshmibai-Sandhya Theorem: the ubiquity of permutation patterns in Schubert calculus and related geometry},
  author={Hiraku Abe and Sara C. Billey},
  journal={arXiv: Combinatorics},
In 1990, Lakshmibai and Sandhya published a characterization of singular Schubert varieties in flag manifolds using the notion of pattern avoidance. This was the first time pattern avoidance was used to characterize geometrical properties of Schubert varieties. Their results are very closely related to work of Haiman, Ryan and Wolper, but Lakshmibai-Sandhya were the first to use that language exactly. Pattern avoidance in permutations was used historically by Knuth, Pratt, Tarjan, and others in… 

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