Texture of One Equality in Neutrino Mass Matrix.

We carry out a phenomenological and analytical study of the texture structures for the Majorana neutrino mass matrix characterized by single equality between two independent matrix elements, with vanishing non-physical phases whose role in the definition we clarify. We find that all textures are viable in both types of hierarchy, except for one inverted hierarchy texture. We also present symmetry realizations for some patterns by using Abelian flavor symmetries within type-I, type-II and mixed type-(I+II) seesaw scenarios.