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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
[2*n*]. 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 2*n*-cycle encoding a Dyck path of length 2*n*.

Received: November 14, 2016.
Accepted: February 17, 2017.
Final version: April 1, 2017.

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