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math.CO2024
A finite totally nonnegative Grassmannian
John Machacek
We introduce totally nonnegative Grassmannians over finite fields where an element of a finite field is nonnegative if it is a square of an element of the finite field. Explicit po…
math.CO2024
Diameter bound for facet-ridge incidence graphs of geometric lattices
Patricia Hersh, John Machacek
This paper proves that the facet-ridge incidence graph of the order complex of any finite geometric lattice of rank has diameter at most . A key ingredient is th…
math.CO2024
Transversal Positroids
John Machacek, George D. Nasr
We exhibit three infinite families of positroids that are transversal matroids. The first comes from a subclass of Postnikov's Le-diagrams that we call Sq-diagrams. Our other two f…