dc.contributor.author | Gadouleau, M | |
dc.contributor.author | Richard, A | |
dc.contributor.author | Riis, S | |
dc.date.accessioned | 2016-04-18T10:46:24Z | |
dc.date.accessioned | 2017-08-08T09:48:15Z | |
dc.date.available | 2017-08-08T09:48:15Z | |
dc.date.issued | 2015-11 | |
dc.date.submitted | 2016-04-05T22:46:23.929Z | |
dc.identifier.citation | Math., S. (2017). Fixed Points of Boolean Networks, Guessing Graphs, and Coding Theory | SIAM Journal on Discrete Mathematics | Vol. 29, No. 4 | Society for Industrial and Applied Mathematics. [online] SIAM Journal on Discrete Mathematics. Available at: http://epubs.siam.org/doi/10.1137/140988358 [Accessed 8 Aug. 2017]. | en_US |
dc.identifier.other | 4 | |
dc.identifier.other | 4 | |
dc.identifier.other | 4 | |
dc.identifier.other | 4 | |
dc.identifier.uri | http://qmro.qmul.ac.uk/xmlui/handle/123456789/25116 | |
dc.description.abstract | In this paper, we are interested in the number of fixed points of functions $f:A^n\to A^n$ over a finite alphabet $A$ defined on a given signed digraph $D$. We first use techniques from network coding to derive some lower bounds on the number of fixed points that only depends on $D$. We then discover relationships between the number of fixed points of $f$ and problems in coding theory, especially the design of codes for the asymmetric channel. Using these relationships, we derive upper and lower bounds on the number of fixed points, which significantly improve those given in the literature. We also unveil some interesting behavior of the number of fixed points of functions with a given signed digraph when the alphabet varies. We finally prove that signed digraphs with more (disjoint) positive cycles actually do not necessarily have functions with more fixed points. | en_US |
dc.format.extent | 2312 - 2335 | |
dc.publisher | SIAM | en_US |
dc.relation.replaces | http://qmro.qmul.ac.uk/xmlui/handle/123456789/11896 | |
dc.relation.replaces | 123456789/11896 | |
dc.relation.replaces | 123456789/11051 | |
dc.relation.replaces | http://qmro.qmul.ac.uk/xmlui/handle/123456789/11051 | |
dc.rights | This is a pre-copyedited, author-produced version of an article accepted for publication in SIAM Journal on Discrete Mathematics following peer review. The version of record is available http://epubs.siam.org/doi/10.1137/140988358 | |
dc.title | Fixed Points of Boolean Networks, Guessing Graphs, and Coding Theory. | en_US |
dc.type | Article | en_US |
dc.rights.holder | © 2015, Society for Industrial and Applied Mathematics Read More: http://epubs.siam.org/doi/10.1137/140988358 | |
dc.identifier.doi | 10.1137/140988358 | |
dc.relation.isPartOf | SIAM J. Discrete Math. | |
dc.relation.isPartOf | SIAM J. Discrete Math. | |
pubs.merge-from | 123456789/11051 | |
pubs.merge-from | http://qmro.qmul.ac.uk/xmlui/handle/123456789/11051 | |
pubs.volume | 29 | |