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math.CO2019★ 8 cited
Basis shape loci and the positive Grassmannian
Cameron Marcott
A basis shape locus takes as input data a zero/nonzero pattern in an matrix, which is equivalent to a presentation of a transversal matroid. The locus is defined as th…
math.CO2018
Combinatorics of the Deodhar decomposition of the Grassmannian
Cameron Marcott
The Deodhar decomposition of the Grassmannian is a refinement of the Schubert, Richardson, and positroid stratifications of the Grassmannian. Go-diagrams are certain fillings of Fe…
math.CO2016
Positroids have the Rayleigh property
Cameron Marcott
The Rayleigh property is a negative correlation property of electrical networks, which was generalized to matroids by Choe and Wagner. We prove that positroids, a class of matroid…