Combinatorics Seminar: Dyck paths and positroids from unit interval orders

Seminar | January 30 | 12:10-1 p.m. | 939 Evans Hall

 Anastasia Chavez and Felix Gotti, UC Berkeley

 Department of Mathematics

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 $2n$.