Research Commons
      • Browse 
        • Communities & Collections
        • Titles
        • Authors
        • By Issue Date
        • Subjects
        • Types
        • Series
      • Help 
        • About
        • Collection Policy
        • OA Mandate Guidelines
        • Guidelines FAQ
        • Contact Us
      • My Account 
        • Sign In
        • Register
      View Item 
      •   Research Commons
      • University of Waikato Research
      • Computing and Mathematical Sciences
      • Computing and Mathematical Sciences Papers
      • View Item
      •   Research Commons
      • University of Waikato Research
      • Computing and Mathematical Sciences
      • Computing and Mathematical Sciences Papers
      • View Item
      JavaScript is disabled for your browser. Some features of this site may not work without it.

      Balanced diagonals in frequency squares

      Cavenagh, Nicholas J.; Mammoliti, Adam
      Thumbnail
      Files
      freqtransfinal.pdf
      Accepted version, 273.1Kb
      DOI
       10.1016/j.disc.2018.04.029
      Find in your library  
      Citation
      Export citation
      Cavenagh, N. J., & Mammoliti, A. (2018). Balanced diagonals in frequency squares. Discrete Mathematics, 341(8), 2293–2301. https://doi.org/10.1016/j.disc.2018.04.029
      Permanent Research Commons link: https://hdl.handle.net/10289/12055
      Abstract
      We 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.
      Date
      2018
      Type
      Journal Article
      Publisher
      Elsevier
      Rights
      This is an author’s accepted version of an article published in the journal: Discrete Mathematics. © 2018 Elsevier.
      Collections
      • Computing and Mathematical Sciences Papers [1452]
      Show full item record  

      Usage

      Downloads, last 12 months
      92
       
       
       

      Usage Statistics

      For this itemFor all of Research Commons

      The University of Waikato - Te Whare Wānanga o WaikatoFeedback and RequestsCopyright and Legal Statement