Latin squares have wide application in communication and cipher. Denote by IdFin(v) the set of all integer pairs (t, s) for which there exist three idempotent Latin squares of order v on the same set having fine structure (t, s). We obtain that (6, 17), (4, 18)∈IdFin(7), which gives some new examples (6, 17), (4, 18)∈Fin(7). We prove that (t, 16)∉IdFin(v) with 0 ≤ t ≤ 3 for order v with 8 ≤ v ≤ 11, and determine the set IdFin(11).
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