6 papers
Sparse Paving Positroids
John Machacek, George D. Nasr
Using Postnikov's Le-diagrams, decorated permutations, and Grassmann necklaces, we classify which positroids are sparse paving matroids. This allows us to enumerate sparse paving p…
Group Actions and Some Combinatorics on Words with
John Machacek
We introduce generalizations of powers and factor complexity via orbits of group actions. These generalizations include concepts like abelian powers and abelian complexity. It is s…
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…
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…
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…
Gorenstein braid cones and crepant resolutions
Joshua Hallam, John Machacek
To any poset , we associate a convex cone called a braid cone. We also associate a fan and study the toric varieties the cone and fan define. The fan always defines a smooth tor…