A combinatorial problem about binary necklaces and attractors of Boolean automata networks
Discrete Mathematics
2016-05-06 v1
Abstract
It is known that there are no more Lyndon words of length n than there are periodic necklaces of same length. This paper considers a similar problem where, additionally, the necklaces must be without some forbidden factors. This problem relates to a different context, concerned with the behaviours of particular discrete dynamical systems, namely, Boolean automata networks. A formal argument supporting the following idea is provided: addition of cycle intersections in network structures causes exponential reduction of the networks' number of attractors.
Cite
@article{arxiv.1605.01505,
title = {A combinatorial problem about binary necklaces and attractors of Boolean automata networks},
author = {Mathilde Noual},
journal= {arXiv preprint arXiv:1605.01505},
year = {2016}
}