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 ofPostnikov, we show that each unit interval order on [n] naturally induces arank n positroid on [2n]. We call the positroids produced in this fashion unitinterval positroids. We characterize the unit interval positroids by describingtheir associated decorated permutations, showing that each one must be a2n-cycle encoding a Dyck path of length 2n.
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