Key points are not available for this paper at this time.
In this paper, we give a formula for the number of permutations that avoid the split patterns 3|12 and 23|1 with respect to a position r. Such permutations count the number of Schubert varieties for which the projection map from the flag variety to a Grassmannian induces a fiber bundle structure. We also study the corresponding bivariate generating function and show how it is related to modified Bessel functions.
Grigsby et al. (Tue,) studied this question.