Geodesic
On $(v,k)$-configurations
Sbornik. Mathematics, Tome 192 (2001) no. 9, pp. 1341-1364

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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. 
@article{SM_2001_192_9_a3,
     author = {F. M. Malyshev and V. E. Tarakanov},
     title = {On $(v,k)$-configurations},
     journal = {Sbornik. Mathematics},
     pages = {1341--1364},
     publisher = {mathdoc},
     volume = {192},
     number = {9},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2001_192_9_a3/}
}
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F. M. Malyshev; V. E. Tarakanov. On $(v,k)$-configurations. Sbornik. Mathematics, Tome 192 (2001) no. 9, pp. 1341-1364. http://geodesic.mathdoc.fr/item/SM_2001_192_9_a3/