The symbolic defect sequence of edge ideals

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dc.contributor.authorReimer, Tessa
dc.contributor.examiningcommitteeCooper, Susanen_US
dc.contributor.examiningcommitteeKirkland, Stephenen_US
dc.contributor.examiningcommitteeZhang, Yangen_US
dc.contributor.supervisorCooper, Susan
dc.date.accessioned2022-08-23T20:53:18Z
dc.date.available2022-08-23T20:53:18Z
dc.date.copyright2022-08-23
dc.date.issued2022-08-23
dc.date.submitted2022-08-23T16:17:38Zen_US
dc.degree.disciplineMathematicsen_US
dc.degree.levelMaster of Science (M.Sc.)en_US
dc.description.abstractSymbolic powers of homogeneous ideals are challenging to study, even for square-free monomial ideals. In particular, the containments between symbolic and ordinary powers of ideals have been widely studied for decades. The symbolic defect provides a measure of the difference between symbolic and ordinary powers of ideals, introduced by Galetto, Geramita, Shin, and Van Tuyl in 2019. In this thesis, we investigate the symbolic defect sequence of edge ideals of nite simple graphs. We classify exactly which terms of this sequence are non-zero and which terms are equal to one. Further, we present formulae for both the rst and second non-zero terms. We describe a complete formula for the symbolic defect sequence of edge ideals of odd cycles, as well as a partial formula for the symbolic defect sequence of edge ideals of unicyclic graphs. We provide both lower and upper bounds on the terms that cannot be computed with this partial formula.en_US
dc.description.noteOctober 2022en_US
dc.description.sponsorshipUniversity of Manitoba Tri-Agency Master's Supplemental Award, Faculty of Graduate Studiesen_US
dc.identifier.urihttp://hdl.handle.net/1993/36734
dc.language.isoengen_US
dc.rightsopen accessen_US
dc.subjectCommutative algebraen_US
dc.subjectEdge idealsen_US
dc.subjectSymbolic powersen_US
dc.subjectSymbolic defecten_US
dc.titleThe symbolic defect sequence of edge idealsen_US
dc.typemaster thesisen_US
local.subject.manitobanoen_US
oaire.awardNumber553378en_US
oaire.awardTitleNSERC CGS Men_US
oaire.awardURIhttps://www.nserc-crsng.gc.ca/students-etudiants/pg-cs/cgsm-bescm_eng.aspen_US
project.funder.identifierhttps://doi.org/10.13039/501100000038en_US
project.funder.nameNational Sciences and Engineering Research Council of Canadaen_US
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