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### Open Access Journals

AMC

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:
combinatorial configuration
,
numerical semigroup.
,
Block design
,
girth
,
partial linear space

## Year of publication

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