20.500.12556/RUL-159728 Barvanja spletov in Goeritzeva matrika m Link colorings and the Goeritz matrix V magistrskem delu obravnavamo vozle in splete v prostoru ter njihove diagrame. Na diagrame spletov ob izbrani Abelovi grupi $A$ vpeljemo Foxova barvanja, Dehnova barvanja, šahovsko senčenje in Goeritzevo matriko. Pokažemo povezave med temi objekti. Grupe Dehnovih barvanj različnih diagramov istega spleta v prostoru so med seboj izomorfne. Prav tako grupe Foxovih barvanj. Pokažemo, kakšna je struktura grupe Foxovih barvanj in struktura grupe Dehnovih barvanj. Obe sta izomorfni direktni vsoti jedra Goeritzeve matrike in ustreznega števila ponovitev grupe $A$, le da je grupa Dehnovih barvanj za en $A$ razsežnejša od grupe Foxovih barvanj. In the master's thesis, we discuss knots and links in space and their diagrams. Fox colorings, Dehn colorings, checkerboard shading, and Goeritz matrix are applied to link diagrams considering the selected Abelian group $A$. We show the connections between these objects. Groups of Dehn colorings of different diagrams of the same link in space are mutually isomorphic. Also groups of Fox colorings. We show the structure of the group of Fox colorings and the structure of the group of Dehn colorings. Both are isomorphic to the direct sum of the kernel of the Goeritz matrix and an appropriate number of copies of the group $A$, except that the group of Dehn colorings contains one more copy of $A$ than the group of Fox colorings. vozel splet Goeritzeva matrika Foxovo barvanje Dehnovo barvanje knot link Goeritz matrix Fox coloring Dehn coloring true false false Slovenski jezik Angleški jezik Magistrsko delo/naloga 2024-07-20 08:15:05 2024-07-20 08:15:09 2024-07-29 08:25:43 0000-00-00 00:00:00 2024 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 140145 202283011 12199.pdf 12199.pdf 1 3DF5F1F90B660C2E5D0BF674F0938EF9 de5c5ac765819bd4fd5c44ab5c0ae6906d22977f72a510824ae693412471cc7c 5c95767d-465f-11ef-8f74-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=187871 12200.pdf 12200.pdf 1 5664EFFEE1D1584FF277D863C651AB70 93a5447a4bbc265dbaa25b3267a06fac437dfd6dd332dd4ef0732dc7532ab3c5 5c95ceb8-465f-11ef-8f74-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=187872 12201.pdf 12201.pdf 1 410F1C4566400978E0162D0BEEA04D5E de4f3dfe8eaf9854b2710e8fdaee80274339de15e4accd63d7c7aa16d0724f83 5c96b8e0-465f-11ef-8f74-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=187873 12202.pdf 12202.pdf 1 8184C3A6B25CF867C25433967D82BD74 e0d48467a9ad19cd12ff4f9dba22fe9b52b434e772fe1e984f7fcf8dbf567fa3 5c96e6b2-465f-11ef-8f74-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=187874 12203.pdf 12203.pdf 1 0BB2934496B6FE07E35A9FAC105CC3BD 1b425bedac6bd732ac7fdc078fc76eee0a280f62b746e62ad6330ad28cd01e3c 5c971136-465f-11ef-8f74-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=187875 Fakulteta za matematiko in fiziko 0 0 0