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New combinatorial objects, which we call (v, k) -configurations, are introduced and studied. They occur as a result of weakening the conditions defining well-known combinatorial objects, the (v, k, lambda) -configurations. Existence results for (v, k) -configurations are proved and methods for constructing them are indicated, based, in particular, upon group-theoretic constructions and quadratic residues modulo a prime. An extended list of examples of (v, k) -configurations, including several infinite series, is presented.
Малышев et al. (Wed,) studied this question.