Séminaire Lotharingien de Combinatoire, 78B.81 (2017), 12 pp.
Anastasia Chavez and Felix Gotti
Dyck Paths and Positroids from Unit Interval Orders
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.
Received: November 14, 2016.
Accepted: February 17, 2017.
Final version: April 1, 2017.
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