Takuro Abe, Toru Yamaguchi
Published 2023-06-20Version 1
We study the free path problem, i.e., if we are given two free arrangements of hyperplanes, then we can connect them by free arrangements or not. We prove that if an arrangement $\mathcal{A}$ and $\mathcal{A} \setminus \{H,L\}$ are free, then at least one of two among them is free. When $\mathcal{A}$ is in the three dimensional arrangement, we show a stronger statement.
Generalization of the addition and restriction theorems from free arrangements to the class of projective dimension one
Free arrangements and coefficients of characteristic polynomials
Matroids with no $U_{2,n}$-minor and many hyperplanes
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