The Existence of latin squares without orthogonal mates

Wanless, Ian M. and Webb, Bridget S. (2006). The Existence of latin squares without orthogonal mates. Designs, Codes and Cryptography, 40(1) pp. 131–135.

DOI: https://doi.org/10.1007/s10623-006-8168-9

Abstract

A latin square is a bachelor square if it does not possess an orthogonal mate; equivalently, it does not have a decomposition into disjoint transversals. We define a latin square to be a confirmed bachelor square if it contains an entry through which there is no transversal. We prove the existence of confirmed bachelor squares for all orders greater than three. This resolves the existence question for bachelor squares.

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About

• Item ORO ID
• 2949
• Item Type
• Journal Item
• ISSN
• 0925-1022
• Keywords
• Latin square; Bachelor square; MOLS; Transversal; Latin trade
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Depositing User
• Bridget Webb