5 papers
Rigidity matroids and linear algebraic matroids with applications to matrix completion and tensor codes
Joshua Brakensiek, Manik Dhar, Jiyang Gao +2
We establish a connection between problems studied in rigidity theory and matroids arising from linear algebraic constructions like tensor products and symmetric products. A specia…
Tilted Richardson Varieties
Jiyang Gao, Shiliang Gao, Yibo Gao
The study of the flag variety and its subvarieties, including Schubert and Richardson varieties, plays a fundamental role in algebraic geometry and algebraic combin…
Characterizing positroid quotients of uniform matroids
Zhixing Chen, Yumou Fei, Jiyang Gao +2
We study two-step flag positroids , where is a quotient of . We provide a complete characterization of all two-step flag positroids that contain a uniform…
On two notions of total positivity for generalized partial flag varieties of classical Lie types
Grant Barkley, Jonathan Boretsky, Christopher Eur +1
For Grassmannians, Lusztig's notion of total positivity coincides with positivity of the Plucker coordinates. This coincidence underpins the rich interaction between matroid theory…
Sandpile Groups of Cayley Graphs of
Jiyang Gao, Jared Marx-Kuo, Vaughan McDonald +1
The sandpile group of a connected graph , defined to be the torsion part of the cokernel of the graph Laplacian, is a subtle graph invariant with combinatorial, algebraic, and g…