Enumerating Permutations Avoiding Split Patterns 3|12 and 23|1

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Abstract

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.

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Grigsby et al. (Tue,) studied this question.

synapsesocial.com/papers/68e77797b6db6435876ec105 https://doi.org/https://doi.org/10.48550/arxiv.2402.17654

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