Latin Squares with a Unique Intercalate |
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| Authors: | Mahamendige Jayama Lalani Mendis Ian M Wanless |
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| Institution: | School of Mathematical Sciences, Monash University, VIC, Australia |
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| Abstract: | Suppose that  and  . We construct a Latin square  of order n with the following properties:  has no proper subsquares of order 3 or more .  has exactly one intercalate (subsquare of order 2) . - When the intercalate is replaced by the other possible subsquare on the same symbols, the resulting Latin square is in the same species as
 . Hence  generalizes the square that Sade famously found to complete Norton's enumeration of Latin squares of order 7. In particular,  is what is known as a self‐switching Latin square and possesses a near‐autoparatopism. |
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| Keywords: | Latin square intercalate autoparatopism self‐switching subsquare |
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