6 papers
Kazhdan-Lusztig polynomials of matroids need not be unimodal
Ronnie Cheng, Shurui Liu
We construct, over every finite field, representable matroids whose Kazhdan-Lusztig polynomials are not unimodal. In particular, the conjectures that all Kazhdan-Lusztig polynomial…
Danus: Orchestrating Mathematical Reasoning Agents with Fact-Graph Memory
Jihao Liu, Guoxiong Gao, Zeming Sun +8
Recent LLM-based mathematical reasoning agents have begun to tackle research-level problems and, in several cases, have contributed to the resolution of open problems. However, sca…
Tangent classes of matroids and wonderful compactifications
Ronnie Cheng, Shurui Liu, Guoxiong Gao
For every loopless matroid and every Feichtner--Yuzvinsky building set containing the top flat, we construct an integral tangent class $T_{M,\mathcal{G}}^{\mathbb…
Tangent classes for matroid building sets
Ronnie Cheng
Significant combinatorial constraints and structure on matroids can come from notions in algebraic geometry, even without the matroids themselves being representable. Let \(M\) be…
Inequalities for Chow Polynomials and Chern Numbers of Matroids
Ronnie Cheng, Wangyang Lin
The Chow polynomial of a matroid is a fundamental invariant whose coefficients exhibit strong positivity properties, including -positivity. We interpret the normalized Chow coe…
On the tangent bundle and the divisor theory of a general matroid
Ronnie Cheng
Extending classical algebro-geometric constructions to arbitrary matroids, we construct a -class for every loopless matroid . When is realizable by a linear…