Enumeration of matrices with prescribed row and column sums
نویسندگان
چکیده
منابع مشابه
Matrices with Prescribed Row and Column Sums
This is a survey of the recent progress and open questions on the structure of the sets of 0-1 and non-negative integer matrices with prescribed row and column sums. We discuss cardinality estimates, the structure of a random matrix from the set, discrete versions of the Brunn-Minkowski inequality and the statistical dependence between row and column sums.
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Let s, t,m, n be positive integers such that sm = tn. Let B(m, s;n, t) be the number of m×n matrices over {0, 1} with each row summing to s and each column summing to t. Equivalently, B(m, s;n, t) is the number of semiregular bipartite graphs with m vertices of degree s and n vertices of degree t. Define the density λ = s/n = t/m. The asymptotic value of B(m, s;n, t) has been much studied but t...
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Let s = (s1, . . . , sm) and t = (t1, . . . , tn) be vectors of nonnegative integer-valued functions of m,n with equal sum S = ∑m i=1 si = ∑n j=1 tj. Let M(s, t) be the number of m × n matrices with nonnegative integer entries such that the ith row has row sum si and the jth column has column sum tj for all i, j. Such matrices occur in many different settings, an important example being the con...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1973
ISSN: 0024-3795
DOI: 10.1016/0024-3795(73)90016-5