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Advances in Mathematics of Communications (AMC)
 

Associating a numerical semigroup to the triangle-free configurations

Pages: 351 - 371, Volume 5, Issue 2, May 2011      doi:10.3934/amc.2011.5.351

 
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Klara Stokes - Universitat Rovira i Virgili, Av. Països Catalans 26, 43007, Tarragona, Catalonia, Spain (email)
Maria Bras-Amorós - Universitat Rovira i Virgili, Av. Països Catalans 26, 43007, Tarragona, Catalonia, Spain (email)

Abstract: It is proved that a numerical semigroup can be associated to the triangle-free $(r,k)$-configurations, and some results on existence are deduced. For example it is proved that for any $r,k\geq 2$ there exists infinitely many $(r,k)$-configurations. Most proofs are given from a graph theoretical point of view, in the sense that the configurations are represented by their incidence graphs. An application to private information retrieval is described.

Keywords:  Block design, combinatorial configuration, partial linear space, girth, numerical semigroup.
Mathematics Subject Classification:  Primary: 05B30; Secondary: 51E30, 20M99.

Received: April 2010;      Revised: March 2011;      Available Online: May 2011.

 References