dc.contributor.advisor | Kazda, Alexandr | |
dc.creator | Šíma, Lucien | |
dc.date.accessioned | 2019-07-12T10:07:36Z | |
dc.date.available | 2019-07-12T10:07:36Z | |
dc.date.issued | 2019 | |
dc.identifier.uri | http://hdl.handle.net/20.500.11956/108041 | |
dc.description.abstract | We investigate delta-matroids which are formed by families of subsets of a finite ground set such that the exchange axiom is satisfied. We deal with some natural classes of delta-matroids. The main result of this thesis establishes sev- eral relations between even, linear, and matching-realizable delta-matroids. Fol- lowing up on the ideas due to Geelena, Iwatab, and Murota [2003], and apply- ing the properties of field extensions from algebra, we prove that the class of strictly matching-realizable delta-matroids, the subclass of matching-realizable delta-matroids, is included in the class of linear delta-matroids. We also show that not every linear delta-matroid is matching-realizable by giving a skew-symmetric matrix representation to the non matching-realizable delta-matroid constructed by Kazda, Kolmogorov, and Rol'ınek [2019]. | en_US |
dc.language | English | cs_CZ |
dc.language.iso | en_US | |
dc.publisher | Univerzita Karlova, Matematicko-fyzikální fakulta | cs_CZ |
dc.subject | delta-matroids | en_US |
dc.subject | exchange axiom | en_US |
dc.subject | constraint satisfaction | en_US |
dc.subject | delta-matroidy | cs_CZ |
dc.subject | axiom o výměně | cs_CZ |
dc.subject | splnitelnost omezení | cs_CZ |
dc.title | Properties of delta-matroids | en_US |
dc.type | bakalářská práce | cs_CZ |
dcterms.created | 2019 | |
dcterms.dateAccepted | 2019-06-21 | |
dc.description.department | Department of Algebra | en_US |
dc.description.department | Katedra algebry | cs_CZ |
dc.description.faculty | Faculty of Mathematics and Physics | en_US |
dc.description.faculty | Matematicko-fyzikální fakulta | cs_CZ |
dc.identifier.repId | 194755 | |
dc.title.translated | Vlastnosti delta-matroidů | cs_CZ |
dc.contributor.referee | Rolínek, Michal | |
thesis.degree.name | Bc. | |
thesis.degree.level | bakalářské | cs_CZ |
thesis.degree.discipline | General Mathematics | en_US |
thesis.degree.discipline | Obecná matematika | cs_CZ |
thesis.degree.program | Mathematics | en_US |
thesis.degree.program | Matematika | cs_CZ |
uk.thesis.type | bakalářská práce | cs_CZ |
uk.taxonomy.organization-cs | Matematicko-fyzikální fakulta::Katedra algebry | cs_CZ |
uk.taxonomy.organization-en | Faculty of Mathematics and Physics::Department of Algebra | en_US |
uk.faculty-name.cs | Matematicko-fyzikální fakulta | cs_CZ |
uk.faculty-name.en | Faculty of Mathematics and Physics | en_US |
uk.faculty-abbr.cs | MFF | cs_CZ |
uk.degree-discipline.cs | Obecná matematika | cs_CZ |
uk.degree-discipline.en | General Mathematics | en_US |
uk.degree-program.cs | Matematika | cs_CZ |
uk.degree-program.en | Mathematics | en_US |
thesis.grade.cs | Výborně | cs_CZ |
thesis.grade.en | Excellent | en_US |
uk.abstract.en | We investigate delta-matroids which are formed by families of subsets of a finite ground set such that the exchange axiom is satisfied. We deal with some natural classes of delta-matroids. The main result of this thesis establishes sev- eral relations between even, linear, and matching-realizable delta-matroids. Fol- lowing up on the ideas due to Geelena, Iwatab, and Murota [2003], and apply- ing the properties of field extensions from algebra, we prove that the class of strictly matching-realizable delta-matroids, the subclass of matching-realizable delta-matroids, is included in the class of linear delta-matroids. We also show that not every linear delta-matroid is matching-realizable by giving a skew-symmetric matrix representation to the non matching-realizable delta-matroid constructed by Kazda, Kolmogorov, and Rol'ınek [2019]. | en_US |
uk.file-availability | V | |
uk.publication.place | Praha | cs_CZ |
uk.grantor | Univerzita Karlova, Matematicko-fyzikální fakulta, Katedra algebry | cs_CZ |
thesis.grade.code | 1 | |