Abstract
Let n ≥ 3 be a positive integer. We show that the number of equivalence classes of generalized Latin squares of order n with n 2 − 1 distinct elements is 4 if n = 3 and 5 if n ≥ 4. It is also shown that all these squares are embeddable in groups. As an application, we obtain a lower bound for the number of isomorphism classes of certain Eulerian graphs with n 2 + 2n − 1 vertices.
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Reference
G. A. Freiman, On two- and three-element subsets of groups, Aequationes Math., 22 (1981), 140–152.
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Communicated by András Sárközy
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Chen, H.V., Chin, A.Y.M. & Sharmini, S. Generalized Latin squares of order n with n 2 − 1 distinct elements. Period Math Hung 66, 105–109 (2013). https://doi.org/10.1007/s10998-012-1690-9
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DOI: https://doi.org/10.1007/s10998-012-1690-9