Lonesum (0,1)-matrices and poly-Bernoulli numbers of negative index
dc.contributor.author | Brewbaker, Chad | |
dc.date | 2019-07-10T01:53:01.000 | |
dc.date.accessioned | 2020-06-30T08:11:35Z | |
dc.date.available | 2020-06-30T08:11:35Z | |
dc.date.copyright | Sat Jan 01 00:00:00 UTC 2005 | |
dc.date.issued | 2005-01-01 | |
dc.description.abstract | <p>This thesis shows that the number of (0,1)-matrices with n rows and k columns uniquely reconstructible from their row and column sums are the poly-Bernoulli numbers of negative index, B[subscript n superscript ( -k)] . Two proofs of this main theorem are presented giving a combinatorial bijection between two poly-Bernoulli formula found in the literature. Next, some connections to Fermat are proved showing that for a positive integer n and prime number p B[subscript n superscript ( -p) congruent 2 superscript n (mod p),] and that for all positive integers (x, y, z, n) greater than two there exist no solutions to the equation: B[subscript x superscript ( -n)] + B[subscript y superscript ( -n)] = B[subscript z superscript ( -n)]. In addition directed graphs with sum reconstructible adjacency matrices are surveyed, and enumerations of similar (0,1)-matrix sets are given as an appendix.</p> | |
dc.format.mimetype | application/pdf | |
dc.identifier | archive/lib.dr.iastate.edu/rtd/18914/ | |
dc.identifier.articleid | 19914 | |
dc.identifier.contextkey | 14540777 | |
dc.identifier.s3bucket | isulib-bepress-aws-west | |
dc.identifier.submissionpath | rtd/18914 | |
dc.identifier.uri | https://dr.lib.iastate.edu/handle/20.500.12876/72866 | |
dc.language.iso | en | |
dc.source.bitstream | archive/lib.dr.iastate.edu/rtd/18914/Brewbaker_ISU_2005_B75.pdf|||Fri Jan 14 21:47:47 UTC 2022 | |
dc.subject.keywords | Computer Science | |
dc.title | Lonesum (0,1)-matrices and poly-Bernoulli numbers of negative index | |
dc.type | article | |
dc.type.genre | thesis | |
dspace.entity.type | Publication | |
thesis.degree.discipline | Computer Science | |
thesis.degree.level | thesis | |
thesis.degree.name | Master of Science |
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