Structure of random 312‐avoiding permutations

@article{Madras2016StructureOR,
  title={Structure of random 312‐avoiding permutations},
  author={Neal Madras and Lerna Pehlivan},
  journal={Random Structures \& Algorithms},
  year={2016},
  volume={49}
}
We evaluate the probabilities of various events under the uniform distribution on the set of 312‐avoiding permutations of 1,…,N . We derive exact formulas for the probability that the ith element of a random permutation is a specific value less than i, and for joint probabilities of two such events. In addition, we obtain asymptotic approximations to these probabilities for large N when the elements are not close to the boundaries or to each other. We also evaluate the probability that the… 
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