Imprimitive matrices of zeros and ones with extremal numbers of ones
نویسندگان
چکیده
منابع مشابه
Matrices of Zeros and Ones
Let A be a. matrix of m rows and n columns and let the entries of A be the integers 0 and 1. We call such a matrix a (0, 1) -matrix of size m by n. The 2 (0, 1)-matrices of size m by n play a fundamental role in a wide variety of combinatorial investigations. One of the chief reasons for this is the following. Let X be a set of n elements Xi, X2, • • • , xn and let Xi, X2, • • • , Xm be m subse...
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Let m and n be positive integers, and let R = (r1, . . . , rm) and S = (s1, . . . , sn) be non-negative integral vectors. Let A(R, S) be the set of all m× n (0, 1)-matrices with row sum vector R and column vector S, and let Ā be the m × n (0, 1)-matrix where for each i, 1 ≤ i ≤ m, row i consists of ri 1’s followed by n − ri 0’s. If S is monotone, the discrepancy d(A) of A is the number of posit...
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Let U(n, T) be the set of ail matrices of O's and l's of order n with exactly r 0's. We obtain an upper bound for the permanent of a matrix in U(n, t). For 0 <r < 2n and for nz-2n C r < n2-n we determine all matrices in U(n, r) with maximum permanent.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2008
ISSN: 0024-3795
DOI: 10.1016/j.laa.2008.02.023