Additional explicit classes of NI circle arrangements

Formulate other explicit classes of normally inductive arrangements of circles beyond the classes produced through Theorems 2 and 3 and Example 4.

Background

The fourth section develops new local changes of labeled Poincaré–Reeb V-digraphs caused by adding circles to NI arrangements. The authors explain that these changes, together with Example 4, yield another explicit class of NI arrangements based on the $(j,\frac{\pi}{4})$-poles of circles.

The paper first introduces labels for Poincaré–Reeb V-digraphs and then asks whether further explicit families of NI circle arrangements can be systematically formulated.