The paper discusses the non-abelian statistics of half-quantum vortices in p-wave superconductors, which are characterized by a zero-energy Majorana fermion in their excitation spectrum. This results in a degeneracy of the ground state of the system of several vortices. The authors derive the non-abelian statistics of these vortices by analyzing the solutions to the Bogoliubov-de-Gennes equations in the vortex core. They show that the non-abelian statistics is identical to that of the Moore-Read (Pfaffian) quantum Hall state, which is also associated with the BCS pairing state. The derivation provides an alternative perspective on the non-abelian statistics and confirms the topological equivalence between the Pfaffian and BCS states. The paper also explores the stability of the Majorana fermion and the non-abelian statistics under various perturbations, highlighting their potential applications in quantum computing.The paper discusses the non-abelian statistics of half-quantum vortices in p-wave superconductors, which are characterized by a zero-energy Majorana fermion in their excitation spectrum. This results in a degeneracy of the ground state of the system of several vortices. The authors derive the non-abelian statistics of these vortices by analyzing the solutions to the Bogoliubov-de-Gennes equations in the vortex core. They show that the non-abelian statistics is identical to that of the Moore-Read (Pfaffian) quantum Hall state, which is also associated with the BCS pairing state. The derivation provides an alternative perspective on the non-abelian statistics and confirms the topological equivalence between the Pfaffian and BCS states. The paper also explores the stability of the Majorana fermion and the non-abelian statistics under various perturbations, highlighting their potential applications in quantum computing.