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Associating a numerical semigroup to the triangle-free configurations
Universitat Rovira i Virgili, Tarragona, Catalonia, Spain.
Universitat Rovira i Virgili, Tarragona, Catalonia, Spain.
2011 (English)In: Advances in Mathematics of Communications, ISSN 1930-5346, Vol. 5, no 2, 351-371 p.Article in journal (Refereed) Published
##### Abstract [en]

It is proved that a numerical semigroup can be associated to the triangle-free $\displaystyle{\left({r},{k}\right)}$-configurations, and some results on existence are deduced. For example it is proved that for any $\displaystyle{r},{k}\geq{2}$ there exists infinitely many $\displaystyle{\left({r},{k}\right)}$-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.

##### Place, publisher, year, edition, pages
2011. Vol. 5, no 2, 351-371 p.
##### Keyword [en]
triangle-free, configuration, partial linear space, numerical semigroup
##### National Category
Discrete Mathematics Algebra and Logic
##### Identifiers
OAI: oai:DiVA.org:liu-91466DiVA: diva2:618011
Available from: 2013-04-25 Created: 2013-04-25 Last updated: 2013-05-06

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Stokes, Klara
##### On the subject
Discrete MathematicsAlgebra and Logic