Criteria for integer and modulo 2 embeddability of graphs to surfaces

可嵌入性与部分矩阵的最小秩

Embeddability of joinpowers, and minimal rank of partial matrices

本文提出了高维复形到流形的Z₂嵌入性准则，将Kühnel问题转化为代数问题，结合了几何拓扑、组合学和线性代数。

The Projective Planarity Question for Matroids of $3$-Nets and Biased Graphs

A biased graph is a graph with a class of selected circles ("cycles", "circuits"), called "balanced", such that no theta subgraph contains exactly two balanced circles. A biased graph has two natural matroids, the frame matroid and the lift matroid. A classical question in matroid theory is whether a matroid can be embedded in a projective geometry. There is no known general answer, but for matroids of biased graphs it is possible to give algebraic criteria. Zaslavsky has previously given such criteria for embeddability of biased-graphic matroids in Desarguesian projective spaces; in this pape…