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arXiv · 0907.4230

The Semigroup of Combinatorial Configurations

Maria Bras-Amorós·Klara Stokes
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Abstract

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.

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Maria Bras-Amorós, Klara Stokes. 2010-12-23. The Semigroup of Combinatorial Configurations. https://arxiv.org/abs/0907.4230

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