標題: THE INTERSECTIONS OF COMMUTATIVE LATIN SQUARES 作者: FU, CMFU, HLGUO, SH應用數學系Department of Applied Mathematics 公開日期: 1-Dec-1991 摘要: A latin square of order n is an nxn array such that each of the integers 1,2,...,n (or any set of n distinct symbols) occurs exactly once in each row and each column. A latin square L = [l(i),j] is said to be commutative provided that l(i),j = l(j),i for all i and j. Two latin squares, L = [l(i),j] and M = [m(i),j], are said to have intersection k if there are exactly k cells (i,j) such that l(i),j = m(i),j. Let I[n] = {0,1,2,...,n2-9,n2-8,n2-6,n2}, H[n] = I[n] union {n2-7,n2-4}, and J[n] be the set of all integers k such that there exists a pair of commutative latin squares of order n which have intersection k. In this paper, we prove that J[n] = I[n] for each odd n greater-than-or-equal-to 7, J[n] = H[n] for each even n greater-than-or-equal-to 6, and give a list of J[n] for n less-than-or-equal-to 5. This totally solves the intersection problem of two commutative latin squares. URI: http://hdl.handle.net/11536/3604 ISSN: 0381-7032 期刊: ARS COMBINATORIA Volume: 32 Issue: 起始頁: 77 結束頁: 96 Appears in Collections: Articles