%0 Journal Article
%T The Semigroup of Combinatorial Configurations
%A Maria Bras-Amor¨Žs
%A Klara Stokes
%J Computer Science
%D 2009
%I arXiv
%X A (v,b,r,k) combinatorial configuration is a (r,k)-biregular bipartite graph with v vertices on the left and b vertices on the right and with no cycle of length 4. Combinatorial configurations have become very important for some cryptographic applications to sensor networks and to peer-to-peer communities. Configurable tuples are those tuples (v,b,r,k) for which a (v,b,r,k) combinatorial configuration exists. It is proved in this work that the set of configurable tuples with fixed r and k has the structure of a numerical semigroup. The numerical semigroup is completely described for r=2 and r=3.
%U http://arxiv.org/abs/0907.4230v3