2017/05/21 by Takuro Abe, Abe, Takuro, Norihiro Nakashima +1
Engineering · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1705.07417
openalex publication_date 2017/05/21 · openalex created_date 2017/11/10 · openalex updated_date 2026/07/28
An m-free hyperplane arrangement is a generalization of a free arrangement. Holm asked the following two questions: (1)Does m-free imply (m+1)-free for any arrangement? (2)Are all arrangements m-free for m large enough? In this paper, we characterize m-freeness for product arrangements, while we prove that all localizations of an m-free arrangement are m-free. From these results, we give answers to Holm's questions.