mycoreobjectrosdok_thesis_0000000054rosdok_thesis_0000000054rosdokthesisrosdok_derivate_00002230592024-11-15T23:00:03.184Z2024-11-13T16:57:35.779ZMCRJANITOReditorFGpublished1rosdok_derivate_0000223059truetruederivate_types:fulltextVolltextfulltextwf_edit_epub wf_register_epubstate:publishedstate:publishedveröffentlichtpublishedrosdok/id000046951908457368Oau2024-11-132024-11-14T10:33:41ZrdaConverted from PICA to MODS using Pica2MODS XSLT Transformer 2.10 [SCM: "f6c168af690edb7cb65ef34e4a2bf7f8714c5d38" "v2.10" "2024-03-28T14:43:08+0100"] with mode 'DEFAULT'.MasterarbeitHochschulschrifto-Polynomials and Explicit Formula for o-MonomialsHyperovals in finite Desarguesian planes of even order q are sets of q+2 points, of which no three are collinear. By association with o-polynomials over binary finite fields, they can be studied algebraically. In this thesis o-polynomials and an equivalence relation based on the equivalence under collineations of the plane are investigated. A second topic is the connection to 2-to-1 polynomials, where explicit formulas for the known o-monomials allow the construction of 2-to-1 binomials. Finally, some generalizations to fields of odd characteristic are made as well.AlexanderOertelVerfasserInautGohar M.Kyureghyan1974 -AkademischeR BetreuerIndgs121242463LucasKrompholzAkademischeR BetreuerIndgsInstitut für Mathematik, Universität Rostock38329-6Universität Rostock1419 - 19761990 -Grad-verleihende Institutiondgg2147083-2Universität Rostock. Mathematisch-Naturwissenschaftliche FakultätGrad-verleihende Institutiondgghttps://purl.uni-rostock.de/rosdok/id00004695urn:nbn:de:gbv:28-rosdok_id00004695-410.18453/rosdok_id00004695510 MathematikMathematisch-Naturwissenschaftliche FakultätCC BY 4.0Nutzungsrechte erteiltLizenz Metadaten: CC0frei zugänglich (Open Access)en1 Online-Ressource (I, 86 Seiten)2024Universität RostockRostockmonographic202420242024Universitätsbibliothek RostockRostock2024Universitätsbibliothek Rostockhttps://purl.uni-rostock.de/rosdok/id00004695Gohar Kyureghyan (Institut für Mathematik, Universität Rostock) ; Lucas Krompholz (Institut für Mathematik, Universität Rostock)[{"name":"Kyureghyan, Gohar","affil":"Institut für Mathematik, Universität Rostock"},{"name":"Krompholz, Lucas","affil":"Institut für Mathematik, Universität Rostock"}]Masterarbeit, Universität Rostock, 2024vorgelegt von Alexander OertelKyureghyan, GoharInstitut für Mathematik, Universität RostockKrompholz, LucasInstitut für Mathematik, Universität Rostockdoctype:epubdoctype:epubDokumenttypDocument typedoctype:epub.masterthesisdoctype:epub.masterthesisMasterarbeitmaster thesisdiniPublType:masterThesis diniPublType2022:MasterThesis XMetaDissPlusThesisLevel:masterinfo:eu-repo/semantics/masterThesisdocumentnatureOfContent:ppn_105825778natureOfContent:ppn_105825778HochschulschriftdiniPublType2022:MasterThesisdiniPublType2022:MasterThesisAbschlussarbeit (Master)master thesisDRIVERXMetaDissPlusThesisLevel:masterXMetaDissPlusThesisLevel:masterMasterarbeitmaster thesisSDNB:510SDNB:510510 Mathematik510 Mathematicsinstitution:unirostockinstitution:unirostockUniversität RostockUniversity of RostockUniversität RostockUniversität RostockUni.Rostockhttp://d-nb.info/gnd/38329-6institution:unirostock.mnfinstitution:unirostock.mnfMathematisch-Naturwissenschaftliche FakultätFaculty of Mathematics and Natural SciencesUniversität Rostock. 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KyureghyanGohar M. Kyureghyanrosdok_thesis_0000000054-d2795893e76Lucas KrompholzLucas Krompholzrosdok_thesis_0000000054-d2795893e87gnd:38329-6Universität RostockUniversität Rostockrosdok_thesis_0000000054-d2795893e101gnd:2147083-2Universität Rostock. Mathematisch-Naturwissenschaftliche FakultätUniversität Rostock. Mathematisch-Naturwissenschaftliche FakultätAlexander OertelGohar M. KyureghyanLucas KrompholzUniversität RostockUniversität Rostock. Mathematisch-Naturwissenschaftliche FakultätAlexander OertelGohar M. KyureghyanLucas KrompholzUniversität RostockUniversität Rostock. Mathematisch-Naturwissenschaftliche FakultätAlexander OertelRostockUniversität Rostockepub.masterthesishttps://purl.uni-rostock.de/rosdok/id00004695urn:nbn:de:gbv:28-rosdok_id00004695-410.18453/rosdok_id00004695Hyperovals in finite Desarguesian planes of even order q are sets of q+2 points, of which no three are collinear. By association with o-polynomials over binary finite fields, they can be studied algebraically. In this thesis o-polynomials and an equivalence relation based on the equivalence under collineations of the plane are investigated. A second topic is the connection to 2-to-1 polynomials, where explicit formulas for the known o-monomials allow the construction of 2-to-1 binomials. Finally, some generalizations to fields of odd characteristic are made as well.20242024Gohar Kyureghyan (Institut für Mathematik, Universität Rostock) ; Lucas Krompholz (Institut für Mathematik, Universität Rostock)[{"name":"Kyureghyan, Gohar","affil":"Institut für Mathematik, Universität Rostock"},{"name":"Krompholz, Lucas","affil":"Institut für Mathematik, Universität Rostock"}]Masterarbeit, Universität Rostock, 2024vorgelegt von Alexander Oertelepub.masterthesis1 Oertel_Master_2024.pdf 1016190 846d785b6a252cd440acd2b31cc35814 rosdok/id000046951908457368Oau2024-11-132024-11-14T10:33:41ZrdaConverted from PICA to MODS using Pica2MODS XSLT Transformer 2.10 [SCM: "f6c168af690edb7cb65ef34e4a2bf7f8714c5d38" "v2.10" "2024-03-28T14:43:08+0100"] with mode 'DEFAULT'.MasterarbeitHochschulschrifto-Polynomials and Explicit Formula for o-MonomialsHyperovals in finite Desarguesian planes of even order q are sets of q+2 points, of which no three are collinear. By association with o-polynomials over binary finite fields, they can be studied algebraically. In this thesis o-polynomials and an equivalence relation based on the equivalence under collineations of the plane are investigated. A second topic is the connection to 2-to-1 polynomials, where explicit formulas for the known o-monomials allow the construction of 2-to-1 binomials. Finally, some generalizations to fields of odd characteristic are made as well.AlexanderOertelVerfasserInautGohar M.Kyureghyan1974 -AkademischeR BetreuerIndgs121242463LucasKrompholzAkademischeR BetreuerIndgsInstitut für Mathematik, Universität Rostock38329-6Universität Rostock1419 - 19761990 -Grad-verleihende Institutiondgg2147083-2Universität Rostock. Mathematisch-Naturwissenschaftliche FakultätGrad-verleihende Institutiondgghttps://purl.uni-rostock.de/rosdok/id00004695urn:nbn:de:gbv:28-rosdok_id00004695-410.18453/rosdok_id00004695510 MathematikMathematisch-Naturwissenschaftliche FakultätCC BY 4.0Nutzungsrechte erteiltLizenz Metadaten: CC0frei zugänglich (Open Access)en1 Online-Ressource (I, 86 Seiten)2024Universität RostockRostockmonographic202420242024Universitätsbibliothek RostockRostock2024Universitätsbibliothek Rostockhttps://purl.uni-rostock.de/rosdok/id00004695Gohar Kyureghyan (Institut für Mathematik, Universität Rostock) ; Lucas Krompholz (Institut für Mathematik, Universität Rostock)[{"name":"Kyureghyan, Gohar","affil":"Institut für Mathematik, Universität Rostock"},{"name":"Krompholz, Lucas","affil":"Institut für Mathematik, Universität Rostock"}]Masterarbeit, Universität Rostock, 2024vorgelegt von Alexander Oertel Kyureghyan, Gohar Institut für Mathematik, Universität Rostock Krompholz, Lucas Institut für Mathematik, Universität Rostock 2024-11-13T16:57:35.779Z 2024-11-15T23:00:03.184Z 2024-11-25T23:00:03.228Z editorFG {"identifier":"rosdok/id00004695","type":"local_id","additional":"","service":"MCRLocalID","created":"2024-11-13T16:57:35.813Z"} {"identifier":"https://purl.uni-rostock.de/rosdok/id00004695","type":"purl","additional":"","service":"RosDokPURL","created":"2024-11-13T16:57:35.844Z","registrationStarted":"2024-11-13T17:25:06.739Z"} {"identifier":"10.18453/rosdok_id00004695","type":"doi","additional":"","service":"RosDokDOI","created":"2024-11-13T16:57:35.851Z","registrationStarted":"2024-11-13T17:25:06.134Z","registered":"2024-11-13T17:25:08.042Z"} {"identifier":"urn:nbn:de:gbv:28-rosdok_id00004695-4","type":"dnbUrn","additional":"","service":"RosDokURN","created":"2024-11-13T16:57:35.837Z","registered":"2024-11-15T13:49:14.083Z"} MCRJANITORfulltextfile/rosdok_thesis_0000000054/rosdok_derivate_0000223059/Oertel_Master_2024.pdfo-Polynomials and Explicit Formula for o-Monomialso-Polynomials and Explicit Formula for o-Monomialsgnd:121242463gnd:38329-6gnd:2147083-2gnd:121242463gnd:38329-6gnd:2147083-2rosdok_thesis_0000000054-d2795893e52Alexander OertelAlexander Oertelrosdok_thesis_0000000054-d2795893e62gnd:121242463Gohar M. KyureghyanGohar M. Kyureghyanrosdok_thesis_0000000054-d2795893e76Lucas KrompholzLucas Krompholzrosdok_thesis_0000000054-d2795893e87gnd:38329-6Universität RostockUniversität Rostockrosdok_thesis_0000000054-d2795893e101gnd:2147083-2Universität Rostock. Mathematisch-Naturwissenschaftliche FakultätUniversität Rostock. Mathematisch-Naturwissenschaftliche FakultätAlexander OertelGohar M. KyureghyanLucas KrompholzUniversität RostockUniversität Rostock. Mathematisch-Naturwissenschaftliche FakultätAlexander OertelGohar M. KyureghyanLucas KrompholzUniversität RostockUniversität Rostock. Mathematisch-Naturwissenschaftliche FakultätAlexander OertelRostockUniversität Rostockepub.masterthesishttps://purl.uni-rostock.de/rosdok/id00004695urn:nbn:de:gbv:28-rosdok_id00004695-410.18453/rosdok_id00004695Hyperovals in finite Desarguesian planes of even order q are sets of q+2 points, of which no three are collinear. By association with o-polynomials over binary finite fields, they can be studied algebraically. In this thesis o-polynomials and an equivalence relation based on the equivalence under collineations of the plane are investigated. A second topic is the connection to 2-to-1 polynomials, where explicit formulas for the known o-monomials allow the construction of 2-to-1 binomials. Finally, some generalizations to fields of odd characteristic are made as well.20242024Gohar Kyureghyan (Institut für Mathematik, Universität Rostock) ; Lucas Krompholz (Institut für Mathematik, Universität Rostock)[{"name":"Kyureghyan, Gohar","affil":"Institut für Mathematik, Universität Rostock"},{"name":"Krompholz, Lucas","affil":"Institut für Mathematik, Universität Rostock"}]Masterarbeit, Universität Rostock, 2024vorgelegt von Alexander Oertel[xslt]Saxonrosdok/id00004695https://purl.uni-rostock.de/rosdok/id00004695190845736810.18453/rosdok_id00004695urn:nbn:de:gbv:28-rosdok_id00004695-4Alexander OertelOertel Alexandero-Polynomials and Explicit Formula for o-MonomialsMasterarbeitmaster thesisUniversität Rostock, 2024Hyperovals in finite Desarguesian planes of even order q are sets of q+2 points, of which no three are collinear. By association with o-polynomials over binary finite fields, they can be studied algebraically. In this thesis o-polynomials and an equivalence relation based on the equivalence under…Alexander Oertelo-Polynomials and Explicit Formula for o-MonomialsUniversitätsbibliothek Rostockhttps://purl.uni-rostock.de/rosdok/id00004695AlexanderOertelVerfasserInautGohar M.Kyureghyan1974 -AkademischeR BetreuerIndgs121242463LucasKrompholzAkademischeR BetreuerIndgsInstitut für Mathematik, Universität Rostock38329-6Universität Rostock1419 - 19761990 -Grad-verleihende Institutiondgg2147083-2Universität Rostock. Mathematisch-Naturwissenschaftliche FakultätGrad-verleihende Institutiondgg[purl]https://purl.uni-rostock.de/rosdok/id00004695[urn]urn:nbn:de:gbv:28-rosdok_id00004695-4[doi]10.18453/rosdok_id00004695open_access20242024epoch:21th_centuryrfc5646:endoctype:epub.masterthesisaccesscondition:openaccessSDNB:510institution:unirostock.mnfstate:published