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Neutrino Mass Matrix from Seesaw Mechanism with Heavy Majorana Neutrino Subject to Texture Zero and Invariant Under a Cyclic Permutation

We evaluate the predictive power of the neutrino mass matrices arising from seesaw mechanism with heavy Majorana mass matrices subject to texture zero and satisfy a cyclic permutation invariant form to the solar neutrino mixing phenomena. From eight possible patterns of heavy Majorana neutrino mass matrix, we found that there is no heavy Majorana neutrino mass matrix to be invariant in form under a cyclic permutation. But, by imposing an additional assumption that at least one of the 2x2 sub-matrices of heavy Majorana neutrino mass matrix inverse having zero determinant, we found that only two of the eight possible patterns for heavy Majorana neutrino mass matrices to be invariant under a cyclic permutation. One of the two invariant heavy Majorana neutrino mass matrices could produces neutrino mass matrix $M_ν$ that can be used to explain the neutrino mixing phenomena for both solar and atmospheric neutrinos qualitatively.