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Properties of Pipe Dreams

  • Evgeny Smirnov,
  • Anna Tutubalina

摘要

Given a permutation 𝑤 ∈ S𝑛, how do we draw a pipe dream (at least one of them) with such a shape? A natural idea would be to arrange crosses and elbow joints in the simplest possible way. For example, we can place all crosses into left-adjusted boxes: i.e., in each row we have a sequence of crosses followed by a sequence of elbow joints.