Abstract
Building upon the work of several previous papers, necessary and sufficient conditions are obtained for an incomplete idempotent latin square R of order n to be embedded in an idempotent latin square of order 2n. This work extends known necessary and sufficient conditions for embeddings into idempotent latin squares of order t≥2n+1, thereby pushing the bounds down to the point where subsequent developments must handle additional conditions that involve the arrangement of symbols on the given square.
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