Abstract: In 2016 Timothy Alland and Edward Richmond gave a permutation pattern avoidance criteria for determining when the projection map from the flag variety to a Grassmannian induces a fiber bundle structure on a Schubert variety. To do this Alland introduced the notion of split pattern avoidance. They proved that a Schubert variety has such a fiber bundle structure if and only if it avoids the split patterns $3|12$ and $23|1$. A natural follow up question is how many permutations in $\mathfrak{S}_n$ avoid these split patterns. In this talk I will present an outline of this result of Alland and Richmond, and discuss my current progress towards counting these split pattern avoiding permutations.
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