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In this paper, we characterize the non-emptiness of the equity core (Selten, 1978) and provide a method, easy to implement, for computing the Lorenz-maximal allocations in the equal division core (Dutta-Ray, 1991) . Both results are based on a geometrical decomposition of the equity core as a finite union of polyhedrons.doi:10.1007/s00186-015-0494-0 fatcat:7eepb34qojeq5c45xy3kaga6nq