Positroids and Graphs
Conference Year
2023
Abstract
Postnikov developed a combinatorial structure of the cells in a totally-nonnegative Grass mannian, which correspond to a special type of ordered matroid, called a positroid. Knutson, Lam and Speyer showed that these positroids are further in bijection with so-called bounded juggling patterns. We focus on graphic matroids, and show that the map provided by this bijection is onto: i.e. there exists a graphic matroid for every bounded juggling pattern.
Primary Faculty Mentor Name
Puck Rombach
Status
Graduate
Student College
College of Engineering and Mathematical Sciences
Program/Major
Mathematics
Primary Research Category
Engineering and Math Science
Positroids and Graphs
Postnikov developed a combinatorial structure of the cells in a totally-nonnegative Grass mannian, which correspond to a special type of ordered matroid, called a positroid. Knutson, Lam and Speyer showed that these positroids are further in bijection with so-called bounded juggling patterns. We focus on graphic matroids, and show that the map provided by this bijection is onto: i.e. there exists a graphic matroid for every bounded juggling pattern.