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Latin Squares with a Unique Intercalate
Author(s) -
Mendis Mahamendige Jayama Lalani,
Wanless Ian M.
Publication year - 2016
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21430
Subject(s) - latin square , mathematics , combinatorics , order (exchange) , square (algebra) , enumeration , intercalation (chemistry) , physics , geometry , chemistry , quantum mechanics , rumen , food science , finance , fermentation , economics
Suppose that n ≡ ± 1mod6 and n ⩾ 7 . We construct a Latin square L n of order n with the following properties:L nhas no proper subsquares of order 3 or more .L nhas 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 asL n . Hence L n generalizes the square that Sade famously found to complete Norton's enumeration of Latin squares of order 7. In particular, L n is what is known as a self‐switching Latin square and possesses a near‐autoparatopism .