dc.contributor.author | Abbe, Emmanuel | |
dc.contributor.author | Spirkl, Sophie | |
dc.date.accessioned | 2022-08-12 00:28:59 (GMT) | |
dc.date.available | 2022-08-12 00:28:59 (GMT) | |
dc.date.issued | 2019 | |
dc.identifier.uri | https://doi.org/10.3390/e21100948 | |
dc.identifier.uri | http://hdl.handle.net/10012/18511 | |
dc.description.abstract | This paper investigates entropic matroids, that is, matroids whose rank function is given as the Shannon entropy of random variables. In particular, we consider p-entropic matroids, for which the random variables each have support of cardinality p. We draw connections between such entropic matroids and secret-sharing matroids and show that entropic matroids are linear matroids when p=2,3 but not when p=9 . Our results leave open the possibility for p-entropic matroids to be linear whenever p is prime, with particular cases proved here. Applications of entropic matroids to coding theory and cryptography are also discussed | en |
dc.description.sponsorship | NSF grant CIF-1706648 | en |
dc.language.iso | en | en |
dc.publisher | Multidisciplinary Digital Publishing Institute | en |
dc.rights | Attribution 4.0 International | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | * |
dc.subject | matroids | en |
dc.subject | entropy function | en |
dc.subject | extremal dependencies | en |
dc.subject | combinatorics | en |
dc.subject | coding | en |
dc.title | Entropic Matroids and Their Representation | en |
dc.type | Article | en |
dcterms.bibliographicCitation | Abbe, E., & Spirkl, S. (2019). Entropic Matroids and Their Representation. Entropy, 21(10), 948. https://doi.org/10.3390/e21100948 | en |
uws.contributor.affiliation1 | Faculty of Mathematics | en |
uws.contributor.affiliation2 | Combinatorics and Optimization | en |
uws.typeOfResource | Text | en |
uws.peerReviewStatus | Reviewed | en |
uws.scholarLevel | Faculty | en |