Séminaire Lotharingien de Combinatoire, 78B.81 (2017), 12 pp.
Anastasia Chavez and Felix Gotti
Dyck Paths and Positroids from Unit Interval Orders
Abstract.
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.
The following versions are available: