Spectral flow for pair compatible equipartitions

We show that a recent spectral flow approach proposed by Berkolaiko–Cox–Marzuola for analyzing the nodal deficiency of partition associated to an eigenfunction can be extended more general partitions. To precise, we work with equipartitions satisfy pair compatible condition. Nodal partitions and minimal are examples such Along way, discuss different approaches Dirichlet-to-Neumann operators: via Aharonov–Bohm operators, double covering argument, slitting domain.