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dc.contributor.authorCavenagh, Nicholas J.en_NZ
dc.contributor.authorMammoliti, Adamen_NZ
dc.date.accessioned2018-09-03T01:56:03Z
dc.date.available2018-08-01en_NZ
dc.date.available2018-09-03T01:56:03Z
dc.date.issued2018en_NZ
dc.identifier.citationCavenagh, N. J., & Mammoliti, A. (2018). Balanced diagonals in frequency squares. Discrete Mathematics, 341(8), 2293–2301. https://doi.org/10.1016/j.disc.2018.04.029en
dc.identifier.issn0012-365Xen_NZ
dc.identifier.urihttps://hdl.handle.net/10289/12055
dc.description.abstractWe say that a diagonal in an array is λ-balanced if each entry occurs λ times. Let L be a frequency square of type F (n; λ); that is, an n ✕ n array in which each entry from {1, 2, …, m=n / λ } occurs λ times per row and λ times per column. We show that if m≤3 , L contains a λ -balanced diagonal, with only one exception up to equivalence when m=2. We give partial results for m≥4 and suggest a generalization of Ryser’s conjecture, that every Latin square of odd order has a transversal. Our method relies on first identifying a small substructure with the frequency square that facilitates the task of locating a balanced diagonal in the entire array.
dc.language.isoenen_NZ
dc.publisherElsevieren_NZ
dc.rightsThis is an author’s accepted version of an article published in the journal: Discrete Mathematics. © 2018 Elsevier.
dc.subjectScience & Technologyen_NZ
dc.subjectPhysical Sciencesen_NZ
dc.subjectMathematicsen_NZ
dc.subjectFrequency squareen_NZ
dc.subjectLatin squareen_NZ
dc.subjectRyser's conjectureen_NZ
dc.subjectTransversalen_NZ
dc.subjectLATIN SQUARESen_NZ
dc.subjectORTHOGONAL MATESen_NZ
dc.titleBalanced diagonals in frequency squaresen_NZ
dc.typeJournal Article
dc.identifier.doi10.1016/j.disc.2018.04.029en_NZ
dc.relation.isPartOfDiscrete Mathematicsen_NZ
pubs.begin-page2293
pubs.elements-id217874
pubs.end-page2301
pubs.issue8en_NZ
pubs.publication-statusPublisheden_NZ
pubs.volume341en_NZ
dc.identifier.eissn1872-681Xen_NZ


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