Quotient of Special Classes of Positroids

Zhixing Chen, Yumou Fei, Jiyang Gao, Yuxuan Sun, Yuchong Zhang

Published 2023-11-09Version 1

In this paper, we give a complete characterization of rank $k-1$ positroids that are quotients of the uniform matroid $U_{k,n}$, completing a partial result by Bendetti-Chavez-Jim\'enez. Furthermore, we show that any pair of positroid quotient with adjacent ranks are related by a cyclic shift on their decorated permutations. We also use the concept of conecklace to give a full characterization of lattice path matroid (LPM) quotient pairs.