Combinatorial Determinants via Contributor Duality

dc.contributor.advisorRusnak, Lucas
dc.contributor.authorDvarishkis, Blake
dc.contributor.committeeMemberCurtin, Eugene
dc.contributor.committeeMemberPatterson, Cody
dc.date.accessioned2023-12-19T17:41:13Z
dc.date.available2023-12-19T17:41:13Z
dc.date.issued2023-12
dc.description.abstractThis thesis gives sentiment to all minors of integer matrix determinant calculations of Laplacian matrices by examining locally signed-graphic behaviors of the associated oriented hypergraph and generalizing the notion of permutations, called contributors. Once contributors are established, we improve on the results of the total-minor polynomial by proving that edge-monicness is sufficient for all contributors. Since signed graphs and ordinary graphs are oriented hypergraphs all their results are subsumed. A study of contributor duality is then the central focus to determine what calculations are universal between both the given oriented hypergraph and its dual. Traditional characteristic polynomial results are then reclaimed as a consequence of contributor duality. These matrices are then placed in a larger universal matrix context to examine their interactions. Finally, the monic condition is adapted to pathing matrices of signed graphs with future work on extending to oriented hypergraphs.
dc.description.departmentMathematics
dc.formatText
dc.format.extent72 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationDvarishkis, B. (2023). Combinatorial determinants via contributor duality (Unpublished thesis). Texas State University, San Marcos, Texas.
dc.identifier.urihttps://hdl.handle.net/10877/17784
dc.language.isoen
dc.subjectdeterminants
dc.subjectcontributors
dc.subjectmathematics
dc.titleCombinatorial Determinants via Contributor Duality
dc.typeThesis
thesis.degree.departmentMathematics
thesis.degree.disciplineMathematics
thesis.degree.grantorTexas State University
thesis.degree.levelMasters
thesis.degree.nameMaster of Science

Files

Original bundle

Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
DVARISHKIS-THESIS-2023.pdf
Size:
1.26 MB
Format:
Adobe Portable Document Format

License bundle

Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
2.56 KB
Format:
Item-specific license agreed upon to submission
Description: