Nonexistence of (3, 2, 1)-conjugate (v+7)-orthogonal Latin squares
نویسندگان
چکیده
Two Latin squares of order v are r-orthogonal if their superposition produces exactly r distinct ordered pairs. If the second square is the (3, 2, 1)-conjugate of the first one, we say that the first square is (3, 2, 1)conjugate r-orthogonal, denoted by (3, 2, 1)-r-COLS(v). The nonexistence of (3, 2, 1)-r-COLS(v) for r ∈ {v + 2, v + 3, v + 5} has been proved by Zhang and Xu [Int. J. Combin. Graph Theory Applic. 2 no. 2 (2009), 103–109]. In this paper, we show the nonexistence of (3, 2, 1)-(v + 7)COLS(v).
منابع مشابه
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ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 52 شماره
صفحات -
تاریخ انتشار 2012