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dc.contributor.advisorWebb, William A.
dc.creatorHaydock, Thomas
dc.date.accessioned2012-04-27T17:43:28Z
dc.date.available2012-04-27T17:43:28Z
dc.date.issued2011
dc.identifier.urihttp://hdl.handle.net/2376/3516
dc.descriptionThesis (Ph.D.), Department of Mathematics, Washington State Universityen_US
dc.description.abstractThis dissertation develops procedures for super fair division that use marks to reduce the number of cuts required for super fair division when compared to all known existing procedures that use marks or can be modified to use marks. Further, our procedures work for the division of desirables, and undesirable, and with entitlements. We further show that for 2 players, at most 3 cuts are required for a super fair division, and we develop a procedure that requires at most 3 cuts for both desirables and undesirable, and with entitlements. For n players, we provide the first known proof that at least n+1 cuts are required for a super fair division, and develop a procedure that requires only 2n+3 cuts, which, to our knowledge, is vast improvement on all known n player procedures. Lastly, we prove that for one of our procedures, the number of cuts required is a function of the number of distinct measures. For the case that there are only 2 distinct measures, the number of cuts achieves the minimum bound of n+1.en_US
dc.description.sponsorshipDepartment of Mathematics, Washington State Universityen_US
dc.languageEnglish
dc.rightsIn copyright
dc.rightsPublicly accessible
dc.rightsopenAccess
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.rights.urihttp://www.ndltd.org/standards/metadata
dc.rights.urihttp://purl.org/eprint/accessRights/OpenAccess
dc.subjectMathematics
dc.subjectFair Division
dc.subjectMinimum Cuts
dc.subjectSuper Fair Division
dc.titleSuper Fair Divisions: A Minimum Number of Cuts
dc.typeElectronic Thesis or Dissertation


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