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On a combinatorial problem in Latin squares. (English) Zbl 0125.28206

Let \(S_n\) be an arbitrary \(n \times n\) Latin square. There exists a principal minor of order not greater than \(C n^{q/(q+1)} (\log n)^{1(q+1)}\) containing every \(q\)-tuple \((a_{i_1},a_{i_2},...,a_{i_q})\) \([i_1,i_2,...,i_q=1,2,...,n\) and all \(i\)-s are different] in some column; \(C\) is a sufficiently large absolute constant. Some unsolved problems connected with this result are formulated.
Reviewer: V.Belousov

MSC:

05B15 Orthogonal arrays, Latin squares, Room squares

Keywords:

combinatorics
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