Geodesic
Pattern Avoidance and Fiber Bundle Structures on Schubert Varieties
Séminaire lotharingien de combinatoire, 78B (2017)

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We give 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. In particular, we show that a Schubert variety has such a fiber bundle structure if and only if the corresponding permutation avoids the split patterns 3|12 and 23|1. We also show that a Schubert variety is an iterated fiber bundle of Grassmannian Schubert varieties if and only if the corresponding permutation avoids (non-split) patterns 3412, 52341, and 635241. 

@article{SLC_2017_78B_a6,
     author = {Timothy Alland and Edward Richmond},
     title = {Pattern {Avoidance} and {Fiber} {Bundle} {Structures} on {Schubert} {Varieties}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {78B},
     year = {2017},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a6/}
}
TY  - JOUR
AU  - Timothy Alland
AU  - Edward Richmond
TI  - Pattern Avoidance and Fiber Bundle Structures on Schubert Varieties
JO  - Séminaire lotharingien de combinatoire
PY  - 2017
VL  - 78B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2017_78B_a6/
ID  - SLC_2017_78B_a6
ER  - 
%0 Journal Article
%A Timothy Alland
%A Edward Richmond
%T Pattern Avoidance and Fiber Bundle Structures on Schubert Varieties
%J Séminaire lotharingien de combinatoire
%D 2017
%V 78B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2017_78B_a6/
%F SLC_2017_78B_a6
Timothy Alland; Edward Richmond. Pattern Avoidance and Fiber Bundle Structures on Schubert Varieties. Séminaire lotharingien de combinatoire, 78B (2017). http://geodesic.mathdoc.fr/item/SLC_2017_78B_a6/