Matrices of zeros and 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...
متن کاملDiscrepancy of Matrices of Zeros and Ones
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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We study the existence of (0, 1)-matrices with given line sums and a fixed zero block. An algorithm is given to construct such a matrix which is based on three applications of the well-known Gale–Ryser algorithm for constructing (0, 1)-matrices with given line sums. A characterization in terms of a certain “structure matrix” is proved. Further properties of this structure matrix are also establ...
متن کامل&mall Diameter Interchange Graphs of Classes of Matrices of Zeros and Ones
Let %I( R, S) denote the class of all m X n matrices of O’s and l’s having row sum vector R and column sum vector S. The interchange graph G( R, S) is the graph where the vertices are the matrices in %(R, S) and where two matrices are joined by an edge provided they differ by an interchange. We characterize those 81 (R, S) for which the graph C( R, S) has diameter at most 2 and those YI( R, S) ...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1960
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1960-10494-6