Enumerating permutations avoiding split patterns 3|12 and 23|1

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...

Full description

Saved in:
Bibliographic Details
Published inDiscrete mathematics Vol. 348; no. 12; p. 114682
Main Authors Grigsby, Travis, Richmond, Edward
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2025
Subjects
Bessel functions
Generating functions
Pattern avoidance
Permutations
Schubert varieties
Schubert varieties
Permutations
Pattern avoidance
Bessel functions
Generating functions
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:0012-365X
DOI:10.1016/j.disc.2025.114682