Geodesic
Dyck Paths and Positroids from Unit Interval Orders
Séminaire lotharingien de combinatoire, 78B (2017)

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It is well known that the number of non-isomorphic unit interval orders on [n] equals the n-th Catalan number. Using work of Skandera and Reed and work of Postnikov, we show that each unit interval order on [n] naturally induces a rank n positroid on [2n]. We call the positroids produced in this fashion unit interval positroids. We characterize the unit interval positroids by describing their associated decorated permutations, showing that each one must be a 2n-cycle encoding a Dyck path of length 2n. 

@article{SLC_2017_78B_a80,
     author = {Anastasia Chavez and Felix Gotti},
     title = {Dyck {Paths} and {Positroids} from {Unit} {Interval} {Orders}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {78B},
     year = {2017},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a80/}
}
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JO  - Séminaire lotharingien de combinatoire
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VL  - 78B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2017_78B_a80/
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%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2017_78B_a80/
%F SLC_2017_78B_a80
Anastasia Chavez; Felix Gotti. Dyck Paths and Positroids from Unit Interval Orders. Séminaire lotharingien de combinatoire, 78B (2017). http://geodesic.mathdoc.fr/item/SLC_2017_78B_a80/