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.

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