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We study some models of the strongly correlated •••Cu-O••• chain fragments that form on the oxygendeficient planes of YBa 2 Cu 3 O 6ϩx . We use analytical and numerical methods to investigate the stability of the chain fragments as a function of their size. We discuss also the size and x dependence of the O-O intrachain interactions that enter in the phenomenological descriptions of the CuO x planes. Only the fermionic degrees of freedom of the chain fragments are considered.

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