2024/03/13 by Daisuke Suyama, Suyama, Daisuke, Michele Torielli +3
Computer Science · Engineering · #05C22 #13N15 #32S22 #52C35 #Advanced Graph Theory Research #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2403.08304
openalex publication_date 2024/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Athanasiadis studied arrangements obtained by adding shifted hyperplanes to the braid arrangement. Similarly, Bailey studied arrangements obtained by adding tilted hyperplanes to the braid arrangement. These two kinds of arrangements are associated with directed graphs and their freeness was characterized in terms of the associated graphs. In addition, there is coincidence of freeness. Namely, if Athanasiadis' arrangement is free, then the corresponding Bailey's arrangement is free, and vice versa. In this paper, we generalize this phenomenon by using gain graphs.