Cavenagh, Nicholas J.Pule, Solomone Tahamano2013-08-292013-08-292013Pule, 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/10289/7922https://hdl.handle.net/10289/7922Let 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.application/pdfenAll items in Research Commons are provided for private study and research purposes and are protected by copyright with all rights reserved unless otherwise indicated.Thesis2013-03-27