The Semigroup of Combinatorial Configurations
Discrete Mathematics
2010-12-24 v3
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.
Cite
@article{arxiv.0907.4230,
title = {The Semigroup of Combinatorial Configurations},
author = {Maria Bras-Amorós and Klara Stokes},
journal= {arXiv preprint arXiv:0907.4230},
year = {2010}
}
Comments
Title changed, article shortened