Abstract: Let $Gr(r, n)$ denote the Grassmannian of $r$-dimensional subspaces of $\mathbb{C^n}$. Each $Gr(r, n)$ contains a unique codimension-1 Schubert subvariety called the Schubert divisor of the Grassmannian. In this talk, we will discuss the correspondence between the set of permutations avoiding the patterns $3412, 52341, 52431$, and $53241$, and the set of Schubert
varieties in the complete flag variety which are iterated fiber bundles of Grassmannians or Grassmannian Schubert divisors. Using this geometrical structure, we calculate the generating function that enumerates the permutations avoiding these patterns.
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