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…
The poset of maximal tubings of the cycle graph is a lattice
Ben Adenbaum, Emily Barnard, Max Hlavacek +4
The poset of maximal tubings of a graph generalizes several well-known and remarkable partial orders. Notable examples include the weak Bruhat order and the Tamari lattice, posets…
IDP for 2-Partition Maximal Symmetric Polytopes
Su Ji Hong, George D. Nasr
We provide a framework for which one can approach showing the integer decomposition property for symmetric polytopes. We utilize this framework to prove a special case which we ref…
Revisiting Dice Relabeling using Cyclotomic Polynomials
Yikai Chao, Josh Gabel, Carlye Larson +1
We continue the exploration of a question of dice relabeling posed by Gallian and Rusin: Given dice, each labeled 1 through , how many ways are there to relabel the dice wit…
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…
On the two-dimensional Jacobian conjecture: Magnus' formula revisited, I
William E. Hurst, Kyungyong Lee, Li Li +1
Let be an algebraically closed field of characteristic 0. When the Jacobian $({\partial f}/{\partial x})({\partial g}/{\partial y}) - ({\partial g}/{\partial x})({\partial f}/{…