Theoretical study of hole-pair system in a periodical lattice

We investigate the statistics of the coupled hole pairs in a crystal lattic e in high T-c superconductors, following the previously developed approach for the collective charge state (holon). The exact commutation relations fo r the hole pair operators correspond to a modified parafermi statistics of rank M' (M' is the number of sites in a "superlattice" formed by centers of mass for each hole pair), i.e, one state can be occupied by up to M' pairs . Even in the absence of dynamic interaction, the system of hole pairs is c haracterized by some immanent interaction (kinematic interaction), which de pends on the hole-pairs concentration. In spite of the kinematic interactio n, there is no statistical prohibition on the Bose-Einstein condensation of coupled hole pairs.