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math.CO2023
One-element Extensions of Hyperplane Arrangements
Hang Cai, Houshan Fu, Suijie Wang
We classify one-element extensions of a hyperplane arrangement by the induced adjoint arrangement. Based on the classification, several kinds of combinatorial invariants including…
math.CO2023
Adjoints of Matroids
Houshan Fu, Chunming Tang, Suijie Wang
We show that an adjoint of a loopless matroid is connected if and only if it itself is connected. Our first goal is to study the adjoint of modular matroids. We prove that a modula…