Erdős, Pál; Ginzburg, A. On a combinatorial problem in Latin squares. (English) Zbl 0125.28206 Publ. Math. Inst. Hung. Acad. Sci., Ser. A 8(1963), 407-411 (1964). 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 Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 Document MSC: 05B15 Orthogonal arrays, Latin squares, Room squares Keywords:combinatorics PDFBibTeX XMLCite \textit{P. Erdős} and \textit{A. Ginzburg}, Publ. Math. Inst. Hung. Acad. Sci., Ser. A 8, 407--411 (1964; Zbl 0125.28206)