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dc.contributor.advisorCavenagh, Nicholas J.
dc.contributor.authorPule, Solomone Tahamano
dc.date.accessioned2013-08-29T21:39:51Z
dc.date.available2013-08-29T21:39:51Z
dc.date.issued2013
dc.identifier.citationPule, S. T. (2013). The number of (0,1) - Matrices with fixed row and column sums (Thesis, Master of Science (MSc)). University of Waikato, Hamilton, New Zealand. Retrieved from https://hdl.handle.net/10289/7922en
dc.identifier.urihttps://hdl.handle.net/10289/7922
dc.description.abstractLet R and S be non-negative and non-increasing vectors of order m and n respectively. We consider the set A(R, S) of all m x n matrices with entries restricted to {0, 1}. We give an alternative proof of the Gale-Ryser theorem, which determines when A(R, S) is non-empty. We show conditions for R and S so that ∣A(R, S) ∣ ∈ {1, n!}. We also examine the case where ∣A(R, S) ∣ = 2 and describe the structure of those matrices. We show that for each positive integer k, there is a possible choice of R and S so that ∣A(R, S) ∣ = k. Furthermore, we explore gm,n(x; y), the generating function for the cardinality ∣A(R, S) ∣ of all possible combinations of R and S.
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.publisherUniversity of Waikato
dc.rightsAll items in Research Commons are provided for private study and research purposes and are protected by copyright with all rights reserved unless otherwise indicated.
dc.titleThe number of (0,1) - Matrices with fixed row and column sums
dc.typeThesis
thesis.degree.grantorUniversity of Waikato
thesis.degree.levelMasters
thesis.degree.nameMaster of Science (MSc)
dc.date.updated2013-03-27T02:16:48Z
pubs.place-of-publicationHamilton, New Zealanden_NZ


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